Electronic Edition Vol. 33, No. 4, 2007

Editors: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao (Houston), H. Brezis (Paris), K. Davidson (Waterloo), C. Hagopian (Sacramento), R. M. Hardt (Rice), J. Hausen (Houston), J. A. Johnson (Houston), W. B. Johnson (College Station), J. Nagata (Osaka), V. I. Paulsen (Houston), Min Ru (Houston), S.W. Semmes (Rice)
Managing Editor: K. Kaiser (Houston)

Revised February 6, 2008.

Houston Journal of Mathematics


Brendan Goldsmith, School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8 Ireland (brendan.goldsmith@dit.ie) and Lutz Strüngmann, Fachbereich 6, Mathematik, Universität Duisburg-Essen, 45117 Essen, Germany (lutz.struengmann@uni-essen.de).
Some transitivity results for torsion abelian groups, pp. 941-957.
We introduce a new class of fully transitive and transitive Abelian p-groups and study the new concept of weak transitivity which is the missing link between full transitivity and transitivity.

L. Fuchs, Department of Mathematics, Tulane University, New Orleans, Louisiana 70118, USA, (fuchs@tulane.edu),
Large indecomposable modules with many automorphisms, pp. 959-966.
ABSTRACT. Over integral domains R admitting fully rigid systems of modules with R as endomorphism rings, we construct indecomposable modules of cardinality κ whose automorphism groups are as large as possible: they have cardinality 2κ. Here κ denotes any infinite cardinal with |R| ≤ κ.
We also show that over certain valuation domains there exist indecomposable divisible torsion modules of arbitrarily large cardinalities κ whose automorphism groups have cardinality 2κ.

Behrooz Khosravi, Dept. of Pure Math., Faculty of Math. and Computer Sci., Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran 15914, IRAN; and Institute for Studies in Theoretical Physics and Mathematics (IPM), (khosravibbb@yahoo.com). and Behnam Khosravi and Bahman Khosravi, Dept. of Math., Faculty of Math. Sci., Shahid Beheshti Univ., Evin, Tehran, 19838, IRAN . 
Groups With the Same Prime Graph as a CIT Simple Group, pp. 967-977.
ABSTRACT. Let G be a finite group. The prime graph of G is the graph whose vertex set is the set of all prime divisors of |G|, and two distinct primes p and q are joined by an edge if and only if G contains an element of order pq. A group M is called a CIT group or a C22 group if M is of even order and the centralizer of any involution is a 2-group. In this paper we determine finite groups G such that their prime graph is the same prime graph of M, where M is a CIT simple group. As a consequence of this result, we prove that if p>7 is a Mersenne prime or a Fermat prime, then PSL(2,p) is uniquely determined by its prime graph. Also we prove a few results by using the main theorem.

Taylor, Michael E., University of North Carolina, Chapel Hill, NC 27599 (met@math.unc.edu).
Scattering Length of Positive Potentials, pp. 979-1003.
ABSTRACT. There is a notion of scattering length of a positive function v on Rn, analogous to the notion of capacity of a compact set K in Rn. Seminal work on this was done in papers of M. Kac and J. Luttinger. This work played an important role in several previous papers of the author on Schrodinger operators. Here we give a systematic presentation of the fundamentals of the subject, and extend its scope from Rn with n bigger than 2 to a natural class of complete Riemannian manifolds, including two-dimensional cases. A central theme is the relation of the scattering length of v to the spectral behavior of v minus the Laplace operator.

Juan de Dios Perez, Universidad de Granada, Spain, (jdperez@ugr.es), Florentino G. Santos, Universidad de Granada, Spain (florenti@ugr.es)  and Young Jin Suh, Kyungpook National University, Korea (yjsuh@mail.knu.ac.kr).
Real hypersurfaces in nonflat complex space forms with commuting structure Jacobi operator, pp. 1005-1009.
ABSTRACT.  We prove the non existence of real hypersurfaces in either complex projective spaces or complex hyperbolic spaces whose structure Jacobi operator commutes with any other Jacobi operator.

Borzellino, Joseph E., California Polytechnic State University, San Luis Obispo, CA 93407 (jborzell@calpoly.edu), Jordan-Squire, Christopher R., Swarthmore College, Swarthmore, PA 19081 (cjordan1@swarthmore.edu), Petrics, Gregory C., Dartmouth College, Hanover, NH 03755 (Gregory.Petrics@dartmouth. edu), and Sullivan, D. Mark, University of Washington, Seattle, WA 98195 (msully@math.washington.edu).
Closed geodesics on orbifolds of revolution., pp. 1011-1025.
ABSTRACT. Using the theory of geodesics on surfaces of revolution, we show that any two-dimensional orbifold of revolution homeomorphic to S2 must contain an infinite number of geometrically distinct closed geodesics. Since any such orbifold of revolution can be regarded as a topological two-sphere with metric singularities, we will have extended Bangert's theorem on the existence of infinitely many closed geodesics on any smooth Riemannian two-sphere. In addition, we give an example of a two-sphere cone-manifold of revolution which possesses a single closed geodesic, thus showing that Bangert's result does not hold in the wider class of closed surfaces with cone manifold structures.

Michał Ryszard Wojcik and Michał Stanisław Wojcik, Institute of Mathematics, Wroclaw University of Technology, Wroclaw, Poland (michal.ryszard.wojcik@gmail.com);(michal.r.wojcik@pwr.wroc.pl).
Characterization of continuity for real valued functions in terms of connectedness, pp. 1027-1031.
ABSTRACT.  In this paper we prove that for any real-valued function defined on a connected topological space being continuous is equivalent to having its graph connected coupled with the complement of the graph being disconnected.

David J. Ryden, Baylor University,  Waco, Texas 76798 (David_Ryden@baylor.edu)
Concerning continua irreducible about finitely many points, pp. 1033-1046.
ABSTRACT. The purpose of this paper is to provide in a unified treatment a number of characterizations for continua and unicoherent continua that are irreducible about finitely many points, and for continua and unicoherent continua that are irreducible about  n points.
One of the main results, from which most of the others follow with relative ease, is that a continuum is irreducible about finitely many points if and only if every pairwise disjoint collection of nonseparating open subsets is finite. Alternate proofs for the classic results of Sorgenfrey are included in the development.

M. de J. Lopez, Facultad de Ciencias Fisico Matematicas, B. U. A. P., Ave. San Claudio y Rio Verde, Ciudad Universitaria, San Manuel Puebla, Pue. C. P. 72570, MEXICO (mtoriz@fcfm.buap.mx), Sergio Macias, Instituto de Matematicas, U. N. A. M., Circuito Exterior, Ciudad Universitaria, M\'exico, D. F., C. P. 04510, MEXIC(macias@servidor.unam.mx).
Induced Maps on n-fold Hyperspaces, pp. 1047-1057.
ABSTRACT. For a given map between continua we study the induced maps between n-fold hyperspaces and between n-fold hyperpsace suspensions.
Our results on n-fold hyperspaces extend some results that are known for the induced maps between the hyperspace of subcontinua.

Gala, Sadek, University of Mostaganem, Department of Mathematics, Box 227, Mostaganem (27000), Algeria. (sadek.gala@gmail.com).
The BMO-1 space and its application to Schechter's inequality, pp. 1059-1066. (Access to this paper is unrestricted)
EDITORIAL STATEMENT. The managing editor has been informed that all of the material in this paper very closely parallels portions of the paper: V.G. Maz'ya and J.E. Verbitsky, Infinitesimal form boundedness and Trudinger's subordination for the Schrödinger operator, Invent. Math. 162 (October 2005), no. 1, 81-136.
Moreover, modulo some minor changes in wording and notation, portions of Gala's paper are identical to corresponding sections in the manuscript of Maz'ya and Verbitsky. The paper of Maz'ya and Verbitsky was posted June 2, 2004 on arXiv
but not cited by Gala.
HJM received Gala's manuscript on September 1, 2005 and, in view of the similarities of content and presentation, we sincerely regret the publication of this paper.

Joiţa, Maria, University of Bucharest, Faculty of Chemistry , Department of Mathematics, Bd. Regina Elisabeta nr. 4-12, Bucharest, Romania (mjoita@fmi.unibuc.ro).
Covariant completely positive linear maps between locally C*-algebras, pp. 1067-1078.
ABSTRACT. We prove a covariant version of the KSGNS (Kasparov, Stinespring, Gel’fand, Naimark, Segal) construction for completely positive linear maps between locally C*-algebras.  As an application of this construction, we show that a covariant completely positive linear map ρ from a locally C*-algebra  A to another locally C*-algebra  B  with  respect to a locally C*-dynamical system  ( G, A, α) extends  to a completely positive linear map on the crossed product  of G and  A  by α.

Sofi, M.A., Kashmir University, Srinagar-190006 (aminsofi@rediffmail.com).
Frechet-valued measures and nuclearity, pp. 1079-1090.
ABSTRACT. The recognition of sequences localised inside the range of a vector measure is an important theme in vector measure theory. In a previous work, the author had characterized Banach spaces X in which absolutely p-summable sequences in X (p>1) are contained inside the range of an X-valued measure of bounded variation precisely as those having (q)-Orlicz property (q being conjugate to p)- a property that characterizes X as finite dimensional as long as p > 2. This motivates the natural question of investigating this property in the setting of Frechet spaces where it is shown to translate into nuclearity -in conformity with the philosophy that nuclear Frechet spaces are better equipped to be called infinite-dimensional variants of finite dimensional spaces than are the more familiar Hilbert spaces. This result provides a strengthening of an earlier result of Bonet and Madrigal, characterising nuclearity of a Frechet space X with absolutely p- summable sequences in X being replaced by null sequences in X. The paper concludes with another useful and more general version of the said result in terms of (p,q)- summing multipliers.

Magajna, Bojan, Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia (Bojan.Magajna@fmf.uni-lj.si).
Injective cogenerators among operator bimodules, pp. 1091-1115.
ABSTRACT. Given C*-algebras A and B acting cyclically on Hilbert spaces H and K, respectively, we characterize completely isometric A,B-bimodule maps from B(K,H) into operator A,B-bimodules. We determine cogenerators in some classes of operator bimodules. For an injective cogenerator X in a suitable category of operator A,B-bimodules we show: if A, regarded as a C*-subalgebra of Al(X) (adjointable left multipliers on X), is equal to its relative double commutant in Al(X), then A must be a W*-algebra.

Kucerovsky, Dan, UNB-F, Fredericton, NB, Canada (dan@math.unb.ca) and Ng, P-W, Fields Institute, 222 College St., Toronto, Canada  (pwn@math.unb.ca).
On nonregular ideals in the multipliers of a stable C*-algebra, pp. 1117-1130.
ABSTRACT. Let B be a unital, separable C*-algebra. Let Z be the centre of B, and let X be the primitive ideal space of B. Suppose that X contains infinitely many distinct points. Then the multipliers of the stabilization of B have a proper, nonregular ideal (we define this concept in the paper). Moreover, if X contains uncountably infinitely many points, then the multipliers of the stabilization have uncountably many distinct, maximal, proper, nonregular ideals. We also give results about Glimm ideals and projections inside ideals of the multipliers of the stabilization

Ilie, Monica, Lakehead University, 955 Oliver Road, Thunder Bay, ON, P7B 5E1, Canada (milie@lakeheadu.ca), and Spronk, Nico, University of Waterloo, Waterloo, ON, N2L 3G1, Canada (nspronk@uwaterloo.ca).
The algebra generated by idempotents in a Fourier-Stieltjes algebra , pp. 1131-1145.
We study the closed algebra BI(G) generated by the idempotents in the Fourier-Stieltjes algebra of a locally compact group G. We show that it is a regular Banach algebra with computable spectrum GI, which we call the idempotent compactification of G. For any locally compact groups G and H, we show that BI(G) is completely isometrically isomorphic to BI(H) exactly when G/Ge= H/He, where Ge and He are the connected components of the identities. We compute some examples to illustrate our results.

Blanchard, Etienne, Institut de Mathématiques, Projet Algèbres d’opérateurs (Plateau 7E), 175, rue du Chevaleret, F-75013 Paris, France, (blanchar@math.jussieu.fr) and Wassermann, Simon, Department of Mathematics, University of Glasgow, Glasgow G12 8QW, United Kingdom (asw@maths.gla.ac.uk)
Exact C*-Bundles, pp. 1147-1159.
Kirchberg and Wassermann showed that if A is an exact continuous C*- bundle on a locally compact Hausdorff space X, then for any other continuous C*-bundle B on X, the minimal tensor product bundle amalgamated over C0(X) of A and B is again continuous. In this paper it is shown conversely that this property characterises the continuous C*-bundles with exact bundle C*-algebra when the base space X has no isolated points. For such X a corresponding result for the maximal tensor product amalgamated over C0(X) of C*-bundles on X is also shown to hold, namely that the maximal tensor product amalgamated over C0(X) of A and B is continuous for all continuous C*-bundles B on X if and only if A has nuclear bundle C*-algebra.

Sarason, Donald, University of California, Berkeley, CA 94720-3840 (sarason@math.berkeley.edu).
The Banach algebra of slowly oscillating functions, pp. 1161-1182.
ABSTRACT. A complex-valued function on the nonnegative real axis is said to be slowly oscillating if it is continuous, bounded, and differs from each of its translates by a function that vanishes at infinity. The family of such functions forms a commutative C*-algebra under the supremum norm. This paper investigates the topology of the Gelfand space of that algebra.

Gao, Mingchu, Louisiana College, Pineville, LA 71360, and College of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi, China (mingchug@yahoo.com).
Clifford algebras over Hilbert C*-Modules, pp. 1183-1214.
ABSTRACT. Clifford algebras of real Hilbert C*-modules with orthonormal bases are introduced. It is showed that the C*-Clifford algebra of a real Hilbert module over a real C*-algebra is *-isomorphic to the spacial tensor product of the complexification C*-algebra and a UHF C*-algebra. The von Neumann Clifford algebra of a real Hilbert module over a von Neumann algebra is*-isomorphic to the von Neumann algebra tensor product of the complexification von Neumann algebra and the hyper-finite type two one factor.

Miklyukov, Vladimir M., Department of Mathematics, Volgograd State University, Universitetskii prospect 100, Volgograd 400062, Russia (miklyuk@mail.ru), Rasila, Antti, Helsinki University of Technology, Institute of Mathematics, P.O.Box 1100, FIN-02015 TKK, Finland (antti.rasila@tkk.fi), and Vuorinen, Matti, Department of Mathematics, FIN-20014 University of Turku, Finland (vuorinen@utu.fi).
Three sphres theorem for p-harmonic functions, pp.1215-1230.
ABSTRACT. Three spheres theorem type result is proved for the p-harmonic functions defined on the complement of k-balls in the Euclidean n-dimensional space.

Kang, Y.H., University of Ulsan, Ulsan 680-749, Korea (yonghann@math.ulsan.ac.kr), Lenhart, S., University of Tennessee, Knoxville, TN 37996-1330 (lenhart@math.utk.edu), and Protopopescu, V., Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6364 (vvp@ornl.gov).
Optimal control of parameters and input functions for nonlinear systems, pp. 1231-1256.
We consider the optimal control problem for both parameters and functions for general nonlinear systems. We show existence of optimal solution and present necessary optimality conditions. We illustrate the approach on two examples.