Electronic Edition Vol. 41, No. 1 , 2015

Editors:  D. Bao (San Francisco, SFSU), D. Blecher (Houston), Bernhard G. Bodmann (Houston), H. Brezis (Paris and Rutgers), B.  Dacorogna (Lausanne), K. Davidson (Waterloo), M. Dugas (Baylor), M. Gehrke (LIAFA, Paris7), C. Hagopian (Sacramento), R. M. Hardt (Rice), Y. Hattori (Matsue, Shimane), W. B. Johnson (College Station),  M. Rojas (College Station), Min Ru (Houston), S.W. Semmes (Rice).
Managing Editor: K. Kaiser (Houston)

 Houston Journal of Mathematics


Dobbs, David E. University of Tennessee, Knoxville, Tennessee 37996-1320, and Shapiro, Jay George Mason University, Fairfax, Virginia 22030-4444, (dobbs@math.utk.edu).
Going down in monoid rings, pp. 1-13.
ABSTRACT. Let A ⊆ B be nonzero commutative unital rings and T ⊆ S torsion-free cancellative abelian monoids. If S and T are groups, then the extension of monoid rings (in this case, group rings) A[T] ⊆ A[S] satisfies GD (the going-down property). We show that if S is of rank 1, then A[S] ⊆ B[S] satisfies GD if and only if the extension of polynomial rings A[X] ⊆ B[X] satisfies GD. Moreover if S is of rank 1, then A[T] ⊆ A[S] satisfies GD. An example shows that the preceding conclusion fails if S and T each have rank 2, with A the field with two elements.

Mooney, Christopher Park, Westminster College, 501 Westminster Avenue, Fulton, Missouri 65251 (christopher.mooney@westminster-mo.edu).
 Generalized factorization in commutative rings with zero-divisors , pp. 15-32.
ABSTRACT. Much work has been done on generalized factorization techniques in integral domains, namely τ-factorization. There has also been substantial progress made in investigating factorization in commutative rings with zero-divisors. This paper seeks to synthesize work done in these two areas and extend the notion of τ-factorization to commutative rings that need not be domains. In addition, we look into particular types of τ relations, which are interesting when there are zero-divisors present. We then proceed to classify commutative rings that satisfy the finite factorization properties given in this paper.

Fritzsch, Karsten, Carl-von-Ossietzky Universität Oldenburg, D-26111 Germany (karsten.fritzsch@uni-oldenburg.de).
An adiabatic decomposition of the Hodge cohomology of manifolds fibred over graphs, pp. 33-58.
ABSTRACT. In this article we use the combinatorial and geometric structure of manifolds with embedded cylinders in order to develop an adiabatic decomposition of the Hodge cohomology of these manifolds. We will on the one hand describe the adiabatic behaviour of spaces of harmonic forms by means of a Cech-de Rham complex defined using a certain graph and on the other hand generalise the Cappell-Lee-Miller splicing map to the case of a finite number of edges, thus combining the topological and the analytic viewpoint.

Konstantina Panagiotidou, Mathematics Division-School of Technology, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece (kapanagi@gen.auth.gr) and Philippos J. Xenos, Mathematics Division-School of Technology, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece (fxenos@gen.auth.gr).
Real hypersurfaces  equipped with pseudoparallel  structure  Jacobi  operator  in  CP2 and CH2, pp. 59-71.
ABSTRACT. We classify real hypersurfaces  equipped with pseudo-parallel structure Jacobi operator.

Sun, Jingzhou, Stony Brook University, Stony Brook, New York 11794-3651(jsun@math.stonybrook.edu).
On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimenional complex projective space, pp. 73-96.
ABSTRACT. Let X be a smooth hypersurface of degree d in the 3-dimenional complex projective space. By totally algebraic calculations, we prove that on the third Demailly-Semple jet bundle of X, the Demailly-Semple line bundle is big for d greater than or equal to 11, and that on the fourth  Demailly-Semple jet bundle of X, the Demailly-Semple line bundle is big for d greater than or equal to 10, improving a recent result of Diverio 

Abrahamsen, Trond A., University of Agder, Norway, Langemets, Johann, University of Tartu, Estonia, Lima, Vegard, Aalesund University College, Norway,  and Nygaard, Olav, University of Agder, Norway (olav.nygaard@uia.no)
On thickness and thinness of Banach spaces,  pp. 97-111.
ABSTRACT. The aim of this note is to complement and extend some recent results on Whitley's indices of thinness and thickness in three main directions. Firstly, we investigate both the indices when forming p-sums of Banach spaces, and obtain formulas which show that they behave rather differently. Secondly, we consider the relation of the indices of the space and a subspace. Finally, every Banach space X containing a copy of c0 can be equivalently renormed so that in the new norm c0 is an M-ideal in X and both the thickness and thinness index of X equal 1.
Corrigendum, added October 8, 2015: The proof of Theorem 4.1 contains a gap. When passing to a subnet, the union  ∪Yn might not be in the subnet. However, when X contains a complemented copy of c0 then X can be renormed such that the result is true. The other results of the paper do not depend on Theorem 4.1
The issue HJM41(4)  contains a detailed proof of this  correction.

Banica, Teodor, Cergy-Pontoise University, 95000 Cergy-Pontoise, France (teo.banica@gmail.com) and Nechita, Ion, Toulouse 3 University, 31062 Toulouse, France (nechita@irsamc.ups-tlse.fr).
Block-modified Wishart matrices and free Poisson laws, pp. 113-134.
ABSTRACT. Topics mentioned in the title are studied.

Bowers, Adam, Department of Mathematics MC 0112, University of California at San Diego, 9500 Gilan Drive, La Jolla, CA 92093-0112 (abowers@ucsd.edu).
Operator-valued measure theory and the Grothendieck inequality, pp. 135-151.
ABSTRACT. We generalize the operator-valued Grothendieck inequality of Defant and Junge by setting it in the context of operator-valued bimeasures. We then prove a duality theorem in the topological setting.

Brown, Jonathan H, Department of Mathematics, University of Dayton, 300 College Park , Dayton, OH 45469-2316 (jonathan.henry.brown@gmail.com), and Goehle, Geoff, Mathematics and Computer Science Department, 300 College Park, Western Carolina University, Cullowhee, NC 28723, and Williams, Dana, Department of Mathematics, 6188 Kemeny Hall, Dartmouth College, Hanover, NH 03755.
Groupoid equivalence and the associated iterated crossed product , pp. 153-175.
ABSTRACT. Given groupoids G and H and a (G, H)-equivalence X we may form the transformation groupoid G × X × H. Given an action of G × X × H on a C*-algebra A we may restrict this action to an action of G×X on A and form the crossed product A×(G×X). We show that there is an action of H on A × G × X and that the iterated crossed product (A × (G × X)) × H is naturally isomorphic to the crossed product A × (G × X × H).

Jesús M. F. Castillo, Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain (castillo@unex.es), Pier Luigi Papini, Via Martucci, 19, 40136 Bologna, Italia (pierluigi.papini@unibo.it),  and Marilda A. Simões, Dipartimento di Matematica " G. Castelnuovo", Universita di Roma " La Sapienza", P.le A. Moro 2, 00185 Roma, Italia (simoes@mat.uniroma1.it).
Thick coverings for the unit ball of a Banach space, pp. 177-186.
ABSTRACT.  We study the behaviour of Whitley's thickness constant of a Banach space with respect to different norms in the product space and we compute it for the classical Banach spaces.

E. Markessinis and P. Valettas, Department of Mathematics, University of Athens, Panepistimioupolis 157-84, Athens, Greece (lefteris128@yahoo.gr), (petvalet@math.uoa.gr).
Distances between classical positions of centrally symmetric convex bodies, pp. 187-211.
ABSTRACT. We study some classical positions (minimal surface area position, minimal mean width position, John's position, Löwner's position and the isotropic position) of a centrally symmetric convex body K in Rn^. Using their isotropic characterizations, we provide upper bounds for the ``trace distance" of any two of them. Most of these bounds are of the order of n1/2.

Raghupathi, Mrinal, Department of Mathematics, United States Naval Academy, Annapolis, MD, 21403 (raghupat@usna.edu) and Wick, Brett D., School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA USA 30332-0160 (wick@math.gatech.ed.
Some remarks about interpolating sequences in reproducing kernel Hilbert spaces , pp. 213-230.
ABSTRACT. In this paper we study two separate problems on interpolation. We first give some new equivalences of Stout's Theorem on necessary and sufficient conditions for a sequence of points to be an interpolating sequence on a finite open Riemann surface. We next turn our attention to the question of interpolation for reproducing kernel Hilbert spaces on the polydisc and provide a collection of equivalent statements about when it is possible to interpolation in the Schur-Agler class of the associated reproducing kernel Hilbert space.

Philip G. Spain, School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow G12 8QW (Philip.Spain@glasgow.ac.uk).
Representations of C*-algebras in dual and right dual Banach algebras, pp. 231-263.
ABSTRACT. The range of a contractive algebra morphism from a C*-algebra to a Banach algebra is closed, and the morphism is a C*-morphism onto its range. When the codomain is a dual Banach algebra, or only a right dual Banach algebra, such a morphism extends to a W*-morphism onto the weak star closure of the range (at least in the unital case).
Boolean algebras of contractive projections (in right dual Banach algebras) have weak star completions; and operators with a contractive functional calculus on a dual Banach space are scalar type prespectral.
Some of these results extend to morphisms that are neither unital nor contractive, so long as one can renorm the codomain dually in a suitable manner, as when the codomain is a dual Banach algebra, or when the range of the natural extension of the morphism forms a commuting set.

Sam Walters, Department of Mathematics & Statistics, University of Northern British Columbia, Prince George, B.C. V2N 4Z9, Canada, http://hilbert.unbc.ca/walters (walters@unbc.ca) .
The exact tracial Rokhlin property, pp. 265-272.
ABSTRACT.It is proved that the noncommutative Fourier transform automorphism σ of the irrational rotation algebra has the exact tracial Rokhlin property - a slightly stronger version of N. Christopher Phillips' tracial Rokhlin property. It essentially means that there are approximately central projections g such that g, σ(g), σ2(g), σ3(g) are mutually orthogonal and 1 - g - σ(g) - σ2(g) - σ3(g) is a `small' projection in the sense that it is Murray von Neumann equivalent to a subprojection of any prescribed projection. Consequently, the flip automorphism and the restriction of the Fourier transform to the flip-fixed subalgebra also have the exact tracial Rokhlin property.

Rongwei Yang and Yixin Yang, Department of Mathematics and Statistics, SUNY At Albany, Albany, NewYork 12222 (ryang@math.albany.edu), (yy281612@albany.edu).
A note on the multivartiable Berger-Shaw theorem, pp. 273-278.
ABSTRACT. For a m-cyclic hyponormal operator T, the Berger-Shaw theo-rem states that the trace of its self-commutator is dominated by a scalar multiple of m. This paper uses an example to show that this kind of dominance is unlikely to exist in multivariable cases. The example uses an inner-sequence-based invariant subspace in Hardy space over the bidisc.

Wagner, Marcus, University of Leipzig, Department of Mathematics, P.O.B. 10 09 20, D-04009 Leipzig, German (marcus.wagner@math.uni-leipzig.de).
Pontryagin's principle for Dieudonné-Rashevsky type problems with polyconvex data, pp. 279-320.
ABSTRACT.In the present paper, we establish Pontryagin's principle for multidimensional control problems of Dieudonné-Rashevsky type in presence of a polyconvex integrand and convex or polyconvex control restrictions. In the proof of the optimality conditions, the polyconvex structure of the data is explicitly used. An application of the theorems to a problem of unimodal hyperelastic image registration is outlined.

Gruenhage, G. , 221 Parker, Auburn University, Auburn AL, 36849 (garyg@auburn.edu) and Hughes, G. 221 Parker, Auburn University, Auburn AL, 36849 (gsh0002@auburn.edu).
Completeness properties in the compact-open topology on fans , pp. 321-337.
ABSTRACT. It is an open problem to characterize those spaces X for which Ck(X), the space of real-valued continuous functions on X with the compact-open topology, has various completeness properties, in particular, the Baire property. We investigate completeness properties of Ck(X) for a class of spaces X having intermediate topologies between the metric and sequential fans. We obtain necessary and sufficient conditions on these X for Ck(X) to be Baire, and show that, except for the sequential fan whose function space is completely metrizable, these Ck(X), while they can be Baire, are never hereditarily Baire or Choquet

Kalapodi, A., Research Academic Computer Technology Institute, University Campus of Patras, Patras 26504, Greece (kalapodi@cti.gr), and Tzannes, V., Department of Mathematics, University of Patras, Patras 26504, Greece (tzannes@math.upatras.gr).
On the set of cut points of Hausdorff maximal connected spaces, pp. 339-346.
ABSTRACT. We construct Hausdorff maximal connected spaces where the  subset of cut points is not dense. The construction is based on the Hausdorff maximal connected space finer than the usual Euclidean topology on the real line, constructed by P. Simon, and on a specific expansion of this space to a maximal Hausdorff one. The required space is obtained by attaching an appropriate closed discrete subset of the Hausdorff maximal connected space to an appropriate closed discrete subset of the Katětov extension of the maximal Hausdorff space.

Liang-Xue Peng (corresponding author) and De-Zhi Kong, Beijing University of Technology, Beijing 100124, China  (pengliangxue@bjut.edu.cn) (L.-X.Peng), (kdz1988@emails.bjut.edu.cn) (D.-Z.Kong).
A note on rectifiable GO-spaces, topological groups, and Gδ-diagonals,
pp. 347-356.
ABSTRACT. If X is a rectifiable GO-space, then the set {tcf(x),tci(x): x∈X} has at most one infinite number. If X is a rectifiable GO-space, then X is metrizable or for any Hausdorff compactification bX the remainder bX\X is countably compact. If X is a rectifiable GO-space and βX \ X is perfect, then X is metrizable. We point out that a result of Peng and He [Theorem 3.7 which appears in Czechoslovak Math. J. 62(137) (2012) 197-214] can be gotten by some results of A.V. Arhangel¡¯skii [Theorem 2.11 and Theorem 1.2 which appear in Fund. Math. 203 (2009) 165-178]. We also point out that a normal remainder of a topological group may not be Lindelöf. This gives a negative answer to a question of A.V. Arhangel¡¯skii [Problem 3.8 which appears in Fund. Math. 203 (2009) 165-178]. In last part of this note, we show that if X is regular and has a Choban operator such that the point e has a countable pseudo-character then X has a regular Gδ-diagonal. If X is a space with a Gδ-diagonal of rank 3 and the cellularity of X is at most c, then |X|≤c. This gives a partial answer to question of A.V. Arhangel¡¯skii and A. Bella [Problem 2 which appears in Applied General Topology, 8(2) (2007) 207-212].

Yan-Kui Song, Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing 210023, China (songyankui@njnu.edu.cn).
Remarks on star-Menger spaces II, pp. 355-364.
ABSTRACT. In this paper, we show that assuming some cardinal assumptions, there exists a Tychonoff strongly star-Menger (hence star-Menger) space having a regular-closed Gδ-subspace which is not star-Menger (hence not strongly star-Menger) which gives a partial answer to a question of Kočinac and a question of Song, and continue to investigate topological properties of star-Menger spaces.