Electronic Edition Vol. 35, No. 2, 2009

Editors: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao (San Francisco, SFSU), H. Brezis (Paris), K. Davidson (Waterloo), M. Gehrke (Radboud), C. Hagopian (Sacramento), R. M. Hardt (Rice), Y. Hattori (Matsue, Shimane), J. Hausen (Houston), J. A. Johnson (Houston), W. B. Johnson (College Station),  V. I. Paulsen (Houston), M. Rojas (College Station), Min Ru (Houston), S.W. Semmes (Rice)
Managing Editor: K. Kaiser (Houston)

Houston Journal of Mathematics


David E. Dobbs, Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300 U.S.A. (dobbs@math.utk.edu).   
When is a pullback a locally divided domain?,
pp. 341-351.
Let P be a property of some (commutative integral) domains such that: if A is a proper subring of a domain B such that Spec(A)= Spec(B) as sets, then A has P if and only if B has P; if A is a domain and Q is a prime ideal of A, then the CPI-extension of A with respect to Q has P if and only if both A/Q and the localization of A at Q have P; and if A is a domain, then A has P if and only if the localization of A at M has P for each maximal ideal M of A. Examples of such P include the property of being a going-down domain and the property of being a locally divided domain. Let T be a domain, Q a maximal ideal of T, p the canonical surjection from T to T/Q, D a subring of T/Q, and R the inverse image of D under p. Then the pullback R (of p and the inclusion map from D to T/Q) has P if and only if both T and D have P. By suitably modifying the above requirements on the property P, we obtain a companion result which applies, in particular, when P is the property of being a locally pseudo-valuation domain.

Maja Fošner, Faculty of logistics, University of Maribor, Mariborska cesta 2, 3000 Celje, Slovenia  (maja.fosner@uni-mb.si), Joso Vukman, Department of Mathematics and Computer Science, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia, (joso.vukman@uni-mb.si).
An equation related to two-sided centralizers in prime rings, pp. 353-361.
ABSTRACT. In this paper we prove the following result: Let R be a prime ring and let T : R → R be an additive mapping satisfying the relation nT(xn)=T(x)xn-1 + xT(x)xn-2 + ... + xn-1T(x) for all x in R where n > 1 is some fixed integer. If char(R) = 0 or n ≤ char(R) ≠ 2, then T is of the form T(x) = λx for all x in R and some fixed element λ in  R where C is the extended centroid of R.

Climent Vidal, Juan, Universidad de Valencia, Departamento de Lógica y Filosofía de la Ciencia, E-46010 Valencia, Spain (juan.b.climent@uv.es) and Soliveres Tur, Juan, Universidad de Valencia, Departamento de Lógica y Filosofía de la Ciencia, E-46010 Valencia, Spain (juan.soliveres@uv.es).
When is the insertion of the generators injective for a sur-reflective subcategory of a category of many-sorted algebras?, pp. 363-372.
ABSTRACT. For a many-sorted signature Σ = (S,Σ) we characterize, by defining the concept of support of an S-sorted set and a convenient algebraic closure operator ExΣ on S, those sur-reflective subcategories K of the category Alg(Σ) of all Σ-algebras for which the unit of the adjunction from SetS to K is pointwise monomorphic.

Strugar, Igor, Limestone College, Gaffney, SC 29340, USA (istrugar@limestone.edu), and Thompson, Gerard, Department of Mathematics, The University of Toledo, Toledo, Ohio 43606, USA (GTHOMPS@UTNet.UToledo.Edu).
Inverse problem for the canonical Lie group connection, pp. 373-409.
ABSTRACT. The geodesic spray of the canonical symmetric connection for a five dimensional Lie group is studied. For each corresponding Lie algebra a faithful representation in terms of vector fields on a five dimensional real space is obtained, thereby providing an effective realization of Lie's third theorem. Thereafter the inverse problem of the calculus of variations for each of the geodesic sprays is investigated. In all cases it is determined whether such spray is of Euler-Lagrange type and in the affirmative case at least one concrete Lagrangian is written down. All the cases where there is a Lagrangian of metric type are exhibited.

Etayo, Fernando, Universidad de Cantabria, 39071, Santander, Spain (etayof@unican.es)  and Santamaría, Rafael, Universidad de León, 24071, León, Spain (rsans@unileon.es).
Connections functorially attached to almost complex product structures, pp. 411-434.
ABSTRACT. Manifolds endowed with three foliations pairwise transversal are known as 3-webs. Equivalently, they can be algebraically defined as biparacomplex or complex product manifolds, i.e., manifolds endowed with three tensor fields of type (1,1), F, P and J=FP, where the two first are product and the third one is complex, and they mutually anti-commute. In this case, it is well known that there exists a unique torsion-free connection parallelizing the structure. In the present paper, we study connections attached to non-integrable almost biparacomplex manifolds

Lan Wu, Renmin University of China, 100872, Beijing, People's Republic of China (wulan@ruc.edu.cn).
A class of variational problem for submanifolds in a space form, pp. 435-450.
ABSTRACT. In this paper we study a class of variational problem for n-dimensional submanifolds in an (n+p)-dimensional unit sphere S, we call M be an extremal submanifold if it satisfies the Euler-Lagrange equation of this variational problem.
we prove an integral inequality of Simons' type for n-dimensional compact extremal submanifolds in an (n+p)-dimensional unit sphere S and
give a characterization of Clifford torus and Veronese surface  by use of our integral inequality. Two special cases were studied by H. Li (2002) and Guo-Li (2007).

Gerardo Acosta, Instituto de Matematicas de la Universidad Nacional Autonoma de Mexico, Circuito Exterior, Area de la Investigacion Cientifica, Mexico D.F., 04510, Mexico (gacosta@matem.unam.mx) and David Herrera-Carrasco, Facultad de Ciencias Físico-MatemAticas de la BenemErita Universidad AutOnoma de Puebla, rio verde y San Claudio, Ciudad Universitaria, Puebla Pue., Mexico (dherrera@fcfm.buap.mx).
Dendrites Without Unique Hyperspace, pp. 451-467.
ABSTRACT.  Let X be a dendrite whose set of end-points is not closed. The second author asked if there is a dendrite Y, not homeomorphic to X, such that the hyperspaces of subcontinua C(X) and C(Y) are homeomorphic. In this paper we answer this question in the positive.

J. Gutiérrez García, Departamento de Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain, (javier.gutierrezgarcia@ehu.es)T. Kubiak, Wydział Matematyki i Informatyki, Uniwersytet im. Adama Mickiewicza, ul. Umultowska 87, 61-614 Poznań, Poland (tkubiak@amu.edu.pl),  and M.A. de Prada Vicente, Departamento de Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain (mariangeles.deprada@ehu.es)
Controlling disjointness with a hedgehog, pp. 469-484.
ABSTRACT. After Frantz's idea of controlling properties of extensions of continuous functions there has been an interest in extending families of continuous pairwise disjoint real-valued functions on normal spaces. We make the observation that disjoint extending a disjoint family of continuous functions is the same thing as extending a single continuous function with values in a hedgehog J(κ) viewed as a bounded complete domain with its Lawson topology where κ is the amount of pairwise disjoint functions which have to be extended. We provide a number of characterizations of spaces for which J(κ) with its Lawson topology becomes an absolute extensor. In particular, this closes the circle of results related to disjoint extension theorems for normal spaces.

Jerzy Krzempek, Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland (j.krzempek@polsl.pl).
Some examples of higher-dimensional rigid continua, pp. 485-500.
ABSTRACT. An attempt is made to find analogues of Anderson, Choquet, and Cook's rigid continua in dimensions greater than one. For each natural number n ≥ 2, two examples of n-dimensional metric continua are presented; the second one is hereditarily indecomposable. Both have the property that for every n-dimensional closed subset P of the continuum in question, call it X, every light continuous map from P into X has a fixed point. Hence, no two disjoint n-dimensional subcontinua of X are homeomorphic.

Rongxin Shen, Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China and Department of Mathematics, Taizhou Teacher's College, Taizhou 225300, P. R. China (srx20212021@163.com) .
On Aleph Zero-weak bases, pp. 501-514.
ABSTRACT. In this paper, the author discusses spaces with certain Aleph Zero-weak bases, gives some characterizations of images of metric spaces by certain quotient maps, and studies the covering properties of spaces with special Aleph Zero-weak bases.

Mora-Corral, Carlos. Mathematical Institute, University of Oxford. Oxford OX1 3LB. UK (mora-cor@maths.ox.ac.uk).
Approximation by piecewise affine homeomorphisms of Sobolev homeomorphisms that are smooth outside a point, pp. 515-539.
This paper is concerned with the problem of approximating in the Sobolev norm a homeomorphism by piecewise affine homeomorphisms. The homeomorphism we want to approximate is supposed to be smooth except at one point. As a corollary of our main result, we prove the following: Let Ω be a subset of  R² be an open set containing 0 with polygonal boundary. Let h: Ω → R² be a Lipschitz homeomorphism such that h-1 is also Lipschitz, h is of class C2 in Ω \ {0} and ||D2h(x)|| = O(|x|-1) as x → 0. Then, for all 1 ≤ p < 2, the function h can be approximated in the norm of the intersection space L ∩ W1,p by a piecewise affine homeomorphism f. Several results in the same spirit are also proved, where we suppose that h and h-1 are smooth except at one point, and their derivatives may have one singularity. The construction of f is explicit. We also show examples of functions satisfying the assumptions of the main theorem of the paper and for which the piecewise affine function on a regular triangulation of Ω that coincides with h at the vertices of the triangulation is not always a homeomorphism.

Rodriguez, Jose, Dpto. de Matematica Aplicada, Facultad de Informatica, Universidad de Murcia, 30100 Espinardo (Murcia), Spain (joserr@um.es).
Convergence theorems for the Birkhoff integral. pp. 541-551.
We study the validity of Vitali's convergence theorem for the Birkhoff integral of functions taking values in a Banach space X. On the one hand, we show that the theorem is true whenever X has weak*-separable dual unit ball. On the other hand, we prove that if X is super-reflexive and has density character the continuum, then there is a uniformly bounded sequence of Birkhoff integrable X-valued functions (defined on [0,1] with the Lebesgue measure) converging pointwise to a non Birkhoff integrable function.

Jiri Spurny, Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic (spurny@karlin.mff.cuni.cz).
Automatic boundedness of affine functions, pp. 553-561.
et f be an affine function on a compact convex set X. We prove that f is bounded provided f has the restricted Baire property on X or is universally Radon measurable on X. We also show that the result of J.P.R. Christensen on weak* universally Baire measurable functionals on spaces of measurable functions can be strengthened for functionals with the restricted Baire property..

Boaz Tsaban, Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel; and Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel, (tsaban@math.biu.ac.il), (http://www.cs.biu.ac.il/~tsaban/) and Lyubomyr Zdomskyy, Department of Mechanics and Mathematics, Ivan Franko Lviv National University, Universytetska 1, Lviv 79000, Ukraine; and Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel (lzdomsky@gmail.com).
On the Pytkeev property in spaces of continuous functions (II), pp. 563-571.
ABSTRACT. We prove that for each Polish space X, the space C(X) of continuous real-valued functions on X satisfies (a strong version of) the Pytkeev property, if endowed with the compact-open topology.
We also consider the Pytkeev property in the case where C(X) is endowed with the topology of pointwise convergence.

Bennett, Grahame, Department of Mathematics, Indiana University, Bloomington, Indiana 47405, U.S.A. (bennettg@indiana.edu).
Meaningful sequences and the Theory of Majorization, pp. 573-589.
ABSTRACT. The fundamental Theorem on Means suggests many new elementary inequalities, yet it offers no hint at all for proving them. Our aim here is to explore this gap, especially in the context of arithmetic progressions. There are applications to the Theory of Majorization.

Aviv Censor, Department of Mathematics, University of California at Riverside, Riverside, CA, 92521, U.S.A. (avivc@math.ucr.edu) and Daniel Markiewicz, Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Beersheva 84105, Israel (danielm@math.bgu.ac.il)
 Limits of groupoid C*-algebras arising from open covers, pp. 591-618.
ABSTRACT. I. Raeburn and J. Taylor have constructed continuous-trace C*-algebras with a prescribed Dixmier-Douady class, which also depend on the choice of a locally finite open cover of the spectrum. We study the asymptotic behavior of these algebras with respect to certain refinements of the cover and appropriate extension of cocycles. This leads to the analysis of a limit groupoid G and a cocycle σ, and the algebra C*(G, σ) may be regarded as a generalized direct limit of the Raeburn-Taylor algebras. As a special case, all UHF C*-algebras arise from this limit construction.

Ciprian Preda, Department of Mathematics, University of California, Los Angeles, CA 90095, U.S.A. (preda@math.ucla.edu).
On the asymptotic behaviour of individual elements under one-parameter semigroups, pp. 619-626.
ABSTRACT. Let T = {T(t)}t≥0 be a strongly continuous semigroup of linear operators on the Banach space X. We point out a sufficient condition to guarantee an exponential decay (as t → ∞) of an individual trajectory t → T(t)x0.

Trond A. Abrahamsen,  Department of Mathematics,  University of Agder, Serviceboks 422, 4604 Kristiansand, Norway (Trond.A.Abrahamsen@uia.no), Vegard Lima, Department of Mathematics, University of Missouri-Columbia,  Columbia, MO 65211, USA (lima@math.missouri.edu), and Åsvald Lima, Department of Mathematics,  University of Agder, Serviceboks 422, 4604 Kristiansand, Norway (Asvald.Lima@uia.no).
Unconditional ideals of finite rank operators II, pp. 627-646.
ABSTRACT. Let E be a subspace of a normed space F. It is known that E is an ideal (resp. a u-ideal) in F if and only if E is an ideal (resp. a u-ideal) in G for every subspace E⊂G⊂F in which E has finite codimension (resp. codimension ≤ 2). We show that in many cases a space of finite rank operators is an ideal (resp. a u-ideal) in a larger space if and only if it is an ideal (resp. a u-ideal) in a space in which it has codimension 1. In particular, we show that F(Y,X) is an ideal (resp. a u-ideal) in W(Y,X**) for all Banach spaces Y if and only if for every reflexive Banach space Y and T in W(Y,X**), F(Y,X) is an ideal (resp. a u-ideal) in span( F(Y,X),{T}).

Johnson, Gerald W., University of Nebraska-Lincoln, Lincoln, NE 68588 (gjohnson2@math.unl.edu) and Kim, Byoung Soo, Seoul  National University of Technology, Seoul 139-743, Korea (mathkbs@snut.ac.kr).
Derivational derivatives and Feynman's operational calculi, pp. 647-664
ABSTRACT. This paper explores the differential (or derivational) calculus associated with the disentangled operators arising from Feynman's operational calculi (FOCi) for noncommuting operators. (We will use the continuous case of the approach to FOCi initiated by Jefferies and Johnson in 2000.) The central part of this paper deals with a first order infinitesimal calculus for a function of n noncommuting operators. Here the first derivatives (or differentials) are replaced by the first order derivational derivatives. The derivational derivatives of the first and higher order have been useful in, for example, operator algebras, noncommutative geometry and Maslov's discrete form of Feynman's operational calculus. In the last section of this paper we will develop some special cases of higher order expansions.

Edmunds, David, School of Mathematical sciences, Cardiff University, Senghennydd Road, Cardiff CF24 4YH, UK (DavidEEdmunds@aol.com), Kokilashvili, Vakhtang, A. Razmadze Mathematical Institute, 1, M. Aleksidze St., 0193 Tbilisi, Georgia; International Black Sea University, Agmashenebeli Kheivani 13 km, 0131 Tbilisi, Georgia (kokil@rmi.acnet.ge), and Meskhi, Alexander, A. Razmadze Mathematical Institute, 1, M. Aleksidze St., 0193 Tbilisi, Georgia; School of Mathematical Sciences, GC University, Lahore 54600, Pakistan (meskhi@rmi.acnet.ge).
Two-Weight estimates in Lp(x) spaces with applications to Fourier series , pp. 665-689.
ABSTRACT. In the present paper we establish sufficient conditions governing two-weighted inequalities for Hardy-Littlewood maximal functions and Calderon-Zygmund operators in variable Lebesgue spaces. Explicit, natural examples are given of pairs of weights that satisfy these conditions.The norm summability of Fourier series and a generalization of Bernstein inequality in a two-weighted setting are proved.