Electronic Edition Vol. 32, No. 1, 2006

Editors: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao (Houston), H. Brezis (Paris), J. Damon (Chapel Hill), 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), , S.W. Semmes (Rice)
Managing Editor: K. Kaiser (Houston)

Houston Journal of Mathematics


Badawi, Ayman, Department of Mathematics and Statistics, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates (abadawi@aus.ac.ae), and Lucas, Thomas G., Department of Mathematics and Statistics, University of North Carolina Charlotte, Charlotte, NC 28223, U.S.A. (tglucas@uncc.edu).
On Φ-Mori Rings, pp. 1-32.
ABSTRACT. A commutative ring R is said to be a φ-ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map φ from the total quotient ring T(R) to R localized at Nil(R). An ideal I that properly contains Nil(R) is φ-divisorial if (φ(R): (φ(R):φ(I)))=φ(I). A ring is a φ-Mori ring if it is a φ-ring that satisfies the ascending chain condition on φ-divisorial ideals. Many of the properties and characterizations of Mori domains can be extended to φ-Mori rings, but some cannot.

Coykendall, Jim, Department of Mathematics, North Dakota State University, Fargo, ND 58105-5075, U.S.A. (jim.coykendall@ndsu.nodak.edu), Dumitrescu, Tiberiu, Facultatea de Matematica, Universitatea Bucuresti, 14 Academiei Str., Bucharest, RO 010014, Romania (tiberiu@al.math.unibuc.ro), and Zafrullah, Muhammad, Department of Mathematics, Idaho State University, Pocatello, ID 83209, U.S.A. (zafrullah@lohar.com).
The half-factorial property and domains of the form A+XB[X], pp. 33-46.
ABSTRACT. In this note, we use the A+XB[X] and A+XI[X] constructions from a new angle to construct new examples of half factorial domains. Positive results are obtained highlighting the interplay between the notions of GCD domain, GL domain, integrally closed domain and half-factorial domain in A+XB[X] constructions. It is additionally shown that constructions of the form A+XI[X] rarely possess the half-factorial property.

F. Fontenele, Departamento de Geometria, Instituto de Matemática, Universidade Federal Fluminense, 24020-140, Niterói, Brazil (fontenele@mat.uff.br), and Sérgio L. Silva, Departamento de Estruturas Matemáticas, Universidade Estadual do Rio de Janeiro, 20550-013, Rio de Janeiro, Brazil (sergiol@ime.uerj.br).
On the m-th mean curvature of compact hypersurfaces, pp. 47-57.
Let M be an n-dimensional compact Riemannian manifold immersed in the (n+1)-dimensional Euclidean space.  In a previous paper, the authors proved that if the product of the scalar curvature by the square of some support function is less than or equal to one then the image of M is a geodesic sphere.  Also we obtained the analogous result in case the ambient is the (n+1)-dimensional hyperbolic space. In this paper, we obtain the correspondent result for immersions into (n+1)-dimensional Euclidean sphere and generalizations of this type of result for high order mean curvatures. The basic technique is to apply the divergence's theorem in a region containing a subset of interest. This technique allows us to give a new proof of a theorem of Vlachos. Some other results are also obtained.

Andreev, Fedor, Western Illinois University, Macomb, IL 61455 (F-Andreev@wiu.edu).
Direct computation of the monodromy data for P6 corresponding to the quantum cohomology of the projective plane , pp. 59-77.
ABSTRACT. A solution to the sixth Painleve equation (P6) corresponding to the quantum cohomology of the projective plane is considered. This is one of the solutions to P6 coming from the Frobenius manifold theory. The resulting generators of the monodromy group are computed. The main difference in the author's approach is its directness, so that no references to the Frobenius manifold theory are needed. The proof presented in the article requires only a) classical results on the asymptotic expansion of some special cases of the hypergeometric function and b) simple, but not obvious rational substitution. The proof also directly demonstrates that the resulting monodromy group is in SL(2,Z).

Muzsnay, Zoltán, University of Debrecen, Debrecen, H-4010, PBox 12, Hungary, (muzsnay@math.klte.hu).
The Euler-Lagrange PDE and Finsler metrizability, pp. 79-98.
ABSTRACT. We investigate the following question: under what conditions can a second-order homogeneous ordinary differential equation (spray) be the geodesic equation of a Finsler space. We show that the Euler-Lagrange partial differential system on the energy function can be reduced to a first order system on this same function. In this way we are able to give effective necessary and sufficient conditions for the local existence of a such Finsler metric in terms of the holonomy algebra generated by horizontal vector-fields. We also consider the Landsberg metrizability problem and prove similar results. This reduction is a significant step in solving the problem whether or not there exists a non-Berwald Landsberg space.

Yoshio Tanaka, Tokyo Gakugei University, Tokyo 184-8501, Japan (ytanaka@u-gakugei.ac.jp), and Ying Ge, Suzhou University, Suzhou 215006, P.R.China (geying@pub.sz.jsinfo.net).
Around quotient compact images of metric spaces, and symmetric spaces, pp. 99-117.
ABSTRACT. We give some new characterizations for certain compact-covering (or sequence-covering) quotient, compact (or ƒÎ-) images of metric spaces in terms of weak bases or symmetric spaces, and consider relations between these compact-covering images and sequence-covering images. Also, we pose some questions around quotient compact images of metric spaces.

Ingram, W. T., University of Missouri - Rolla, Rolla, MO 65409-0020 (ingram@umr.edu), and Mahavier, William S., Emory University, Atlanta, GA 30322 (wsm@mathcs.emory.edu).
Inverse Limits of Upper Semi-continuous Set Valued Functions, pp. 119-130.
ABSTRACT. In this article we define the inverse limit of an inverse sequence (X11), (X22), (X33), ... where each Xi is a compact Hausdorff space and each ƒi is an upper semi-continuous function from Xi+1 into 2Xi . Conditions are given under which the inverse limit is a Hausdorff continuum and examples are given to illustrate the nature of these inverse limits.

S. Oltra and E.A. Sanchez Perez, Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Valencia 46071, Spain (soltra@mat.upv.es), (easancpe@mat.upv.es).
Order properties and p-metrics on Köthe function spaces, pp. 131-142.
ABSTRACT. If L is a Köthe function space, we define and characterize a class of p-pseudo metrics on L using the representation of the dual space by means of integrals. We show that it provides an adequate framework for the study of the relation between the to pology and the order on L. In particular, we obtain in this context new characterizations of the lattice properties of L. We a lso show that these results can be applied in the case of the dual complexity spaces that are used as models for the complexity analysis of algorithms and programs in Theoretical Computer Science.

Milutinovic, Uros, University of Maribor, PEF, Koroska 160, 2000 Maribor, Slovenia (uros.milutinovic@uni-mb.si).
Approximation of maps into Lipscomb's space by embeddings, pp. 143- 159.
ABSTRACT. Let J(t) be Lipscomb's one-dimensional space and let Ln(t) be Lipscomb's n-dimensional universal space of weight t, i.e. the set of all elements of J(t)n+1 having at least one irrational coordinate. In this paper we prove that if X is a metrizable space and dim X≤n, wX ≤t, then any mapping from X to J(t)n+1 can be approximated arbitrarily close by an embedding from X to Ln(t). Also, in the separable case an analogous result is obtained, in which the classic triangular Sierpinski curve (homeomorphic to J(3)) is used instead of J(aleph0).

S. Macias, Instituto de Matematicas, U.N.A.M., Circuito Exterior, Ciudad Universitaria, Mexico, D.F., C.P. 04510 (macias@servidor.unam.mx)..
A class of one-dimensional, nonlocally connected continua for which the set function T is continuous, pp. 161-165.
ABSTRACT. We present a class of one--dimensional, nonlocally connected continua for which the set function T is continuous.

B. Mond, Department of Mathematics, La Trobe University, Bundoora, Vic. 3083, Australia (b.mond@latrobe.edu.au), J. Pevcaric, Faculty of Textile Technology, University of Zagreb, 10000 Zagreb, Croatia, and I. Peric, Faculty of Chemical Engineering & Technology, University of Zagreb, 10000 Zagreb, Croatia, (iperic@pbf.hr).
On Reverse Integral Mean Inequalities, pp. 167-181.
ABSTRACT. If f s a positive integrable function, then it is well-known that for real numbers p and q, q≤p, the ratio of the p-power integral mean of f by the q-power integral mean is greater than or equal to 1. Different authors have given reverse inequalities for this ratio. Here we present various upper bounds for this ratio for a wider class of weighted power means and functions. These results are extensions of results of Muckenhoupt, Nania and Alzer.

Isaac Pesenson, Department of Mathematics, Temple University, Philadelphia, PA 19122 (pesenson@math.temple.edu).
Deconvolution of band limited functions on non-compact symmetric spaces, pp. 183-204.
ABSTRACT. It is shown that a band limited function on a non-compact symmetric space can be reconstructed in a stable way from some countable sets of values of its convolution with certain distributions of compact support. A reconstruction method in terms of frames is given which is a generalization of the classical result of Duffin-Schaeffer about exponential frames on intervals. The second reconstruction method is given in terms of polyharmonic average splines.

Boos, Johann, FernUniversität in Hagen, D-58084 Hagen, Germany (Johann.Boos@FernUni-Hagen.de), and Leiger, Toivo, Puhta Matemaatika Instituut, Tartu Ülikool, EE 50090 Tartu, Eesti (Toivo.Leiger@ut.ee), and Zeltser, Maria, Matemaatika osakond, Tallinna Ülikool, EE 10120 Tallinn, Eesti (mariaz@tln.ee).
The intersection of matrix domains including a given sequence space, pp. 205-225.
ABSTRACT. On the one hand, Hahn's theorem tells that each convergence domain containing the set of all sequences of 0's and 1's includes all bounded sequences. On the other hand, it is easy to verify that for each unbounded sequence x there exists a convergence domain that includes all bounded sequences but does not contain x. Thus the set of all bounded sequences is the intersection of all convergence domains containing all sequences of 0's and 1's. In this sense the set of all bounded sequences is the `summability hull' of the set of all sequences of 0's and 1's. In the present paper the `summability hull' of arbitrarily given sequence spaces is studied.

Anna, Kaminska, Department of Mathematical Sciences, The University of Memphis, Memphis, USA (kaminska@memphis.edu) and Han Ju, Lee, Department of Mathematics, POSTECH, Pohang-shi, Republic of Korea (hahnju@postech.ac.kr).
On uniqueness of extension of homogeneous polynomials, pp. 227-252.
ABSTRACT. We study the uniqueness of norm-preserving extension of n-homogeneous polynomials in Banach spaces. We show that norm-preserving extensions of n-homogeneous polynomials do not need to be unique for n > 1 in real Banach spaces, and for n> 2 in a large class of complex Banach function spaces. We find further a geometric condition, which in particular yields that a unit ball in X does not possess any complex extreme point, under which for every norm-attaining 2-homogeneous polynomial on a complex symmetric sequence space X there exists a unique norm-preserving extension from X to its bidual. In particular, if M is a Marcinkiewicz sequence space and m is its subspace of order continuous elements, we show that every norm-attaining 2-homogeneous polynomial on m has a unique norm-preserving extension to its bidual M if and only if no element of a unit ball of m is a complex extreme point of its unit ball. We then apply these results to obtain some necessary conditions for the uniqueness of extension of 2-homogeneous polynomials from a complex symmetric space X to its bidual.

Englis, Miroslav, MU AV CR, Zitna 25, 11567 Praha 1, Czech Republic (englis@math.cas.cz), Hänninen, Teemu T., Department of Mathematics, University of Helsinki, P.O. Box 4, 00014 Helsinki, Finland (Teemu.Hanninen@helsinki.fi), and Taskinen, Jari, Department of Mathematics, University of Joensuu, P.O. Box 111, 80101 Joensuu, Finland; current address: Dept. of Mathematics, Univ. of Helsinki, P.O.Box 4, 00014 Helsinki, Finland (jari.taskinen@helsinki.fi).
Minimal L-infinity-type spaces on strictly pseudoconvex domains on which the Bergman projection is continuous , pp. 253-275.
ABSTRACT. We describe the space of functions on a smoothly bounded strictly pseudoconvex domain such that (i) the Bergman projection is continuous on it; (ii) its topology is given by a family of weighted sup-norms, with weights depending only on a given defining function; (iii) it contains all bounded measurable functions; and (iv) it is contained continuously into any other function space satisfying (i)-(iii). This generalizes the results obtained by the third author for the unit disc. We also obtain analogous assertions for the standard weighted Bergman projections, and, under the additional hypothesis that the domain be complete circular, also for the Szegö projection on pluriharmonic functions.

Steven M. Seubert, Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403-0221 (sseuber@bgnet.bgsu.edu).
Dissipative compressed Toeplitz operators on shift co-invariant subspaces , pp. 277-292.
ABSTRACT. Necessary and sufficient conditions for an operator commuting with the compression of the standard unilateral shift on the Hardy space H2 to a shift co-invariant subspace to be dissipative are given in terms of the coset of symbols of the operator. The lattice of closed invariant subspaces of a dissipative operator commuting with the compression of the shift operator is shown to coincide with the lattices of closed invariant subspaces of the fractional powers of the dissipative operator using semigroup results. Sufficient conditions for the lattice of closed invariant subspaces of a dissipative operator commuting with the compression of the shift operator to coincide with the lattice of closed invariant subspaces of the compression of the shift operator are given whenever the shift co-invariant subspace corresponds to a Blaschke product.

Jim Gleason, Department of Mathematics, University of Tennessee, Knoxville, TN, USA 37996-1300 (gleason@math.utk.edu). Current address: Department of Mathematics, The University of Alabama, Tuscaloosa, AL 35487-0350 (jgleason@as.ua.edu).
Quasinormality of Toeplitz Tuples with Analytic Symbols, pp. 293-298.
ABSTRACT. We study properties of quasinormality for tuples of Toeplitz operators with analytic symbols on the Hardy and Bergman space of the unit ball or the polydisc in C. Also, using examples we show that different notions of quasinormality for commuting tuples of operators correspond to multiplication by the coordinate functions on different domains in C.

Kamila Klis, and Marek Ptak, Institute of Mathematics, University of Agriculture, Al. Mickiewicza 24/28, 30-059 Krakow, Poland (rmklis@cyf-kr.edu.pl), (rmptak@cyf-kr.edu.pl).
k-Hyperreflexive subspaces, pp. 299-313.
ABSTRACT. Changing rank-one operators in a suitable definition of hyperreflexivity to rank k operators we give a definition of k-hyperreflexivity. We give an example of 2-hyperreflexive subspace which second ampliation is not hyperreflexive. There are also given properties and examples of k-hyperreflexivity. It is shown that the space of all Toeplitz operators is 2-hyperreflexive and each k-dimensional subspace is k-hyperreflexive.

Bernal-Gonzalez and Calderon-Moreno, M.C., Departamento de Analisis Matematico. Facultad de Matematicas, apdo. 1160. Avenida Reina Mercedes, 41080 Sevilla , Spain (lbernal@us.es), (mccm@us.es) and Luh, W., Fachbereich Mathematik, Universität Trier, D-54286 Trier, Germany (luh@uni-trier.de}.
Universal matrix transforms of holomorphic functions , pp. 315-324.
ABSTRACT. The phenomenon of overconvergence is related with the convergence of subsequences of the sequence of partial sums of Taylor series at points outside their disk of convergence. During the seventies Chui and Parnes and the third author provided a holomorphic function in the unit disk which is universal with respect to overconvergence. The generic nature of this kind of universality has been recently shown by Nestoridis. In this paper, we connect the overconvergence with the summability theory. We show that there are “many” holomorphic functions in the unit disk such that their sequences of A-transforms have the overconvergence property, A being an infinite matrix. This strengthens Nestoridis' result.