*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), J. Nagata (Osaka), V. I. Paulsen (Houston), G. Pisier (College
Station and Paris), S. W. Semmes (Rice)
*Managing Editor*: K. Kaiser (Houston)

Houston Journal of Mathematics

**Manfred Dugas, ** Department of Mathematics, Baylor University, Waco,
Texas 76798 (Manfred_Dugas@baylor.edu) and ** Shalom Feigelstock, **
Department of Mathematics, Bar Ilan University, Ramat Gan 52600, Israel
(feigel@macs.biu.ac.il).

Co-minimal Abelian Groups,
pp. 637-648.

ABSTRACT.
An abelian group A was called minimal in [1], if A is isomorphic to all its
subgroups of finite index. We study the dual notion and call A co-minimal if A
is isomorphic to A/K for all finite subgroups K of A . We will see that minimal
and co-minimal groups exhibit a similar behavior in some cases, but there are
several differences. While a reduced p -group A is minimal if and only if A/p^{ω}
is minimal, this no longer holds for co-minimal p -groups. We show that a
separable p -group A is co-minimal if and only if A is minimal. This does not
hold for p -groups with elements of infinite height. We find necessary
conditions for co-minimal p -groups in terms of their Ulm-Kaplansky invariants,
which are also sufficient for totally projective p -groups. If A is a mixed
group with a knice system, also known as Axiom 3 modules, then A is co-minimal
if and only if t(A), the torsion part of A, is co-minimal. We construct an
example of a mixed group A such that t(A) is a totally projective p -group of
length ω+1 such that t(A) is co-minimal but A is not co-minimal. Moreover, we
construct p -groups G of length ω+1 such that all Ulm-Kaplansky invariants of G
are infinite, i.e. G is minimal, but G is not co-minimal.

*Reference*:
**[1]** B. Goldsmith and S.OhOgain, *On torsion and mixed
minimal abelian groups,* Rocky Mountain J. Math.
**32** (2002), 1451-1465.

**B. Fine,
** Department of Mathematics, Fairfield University, Fairfield, CT 06430 and **
Anthony M. Gaglione,**
Department of Mathematics, U.S. Naval Academy, Annapolis, MD 21402
(amg@usna.edu) and **D. Spellman,** Department of Mathematics,
Temple University, Philadelphia, PA 19122.

Discriminating and Squarelike Groups
II: Examples, pp. 649-674.

ABSTRACT.
Discriminating groups were invented by G. Baumslag, A.G. Myasnikov and V.N.
Remeslennikov. These groups arose out of consideration by the above authors of
their freshly minted theory of algebraic geometry over groups. Although
unforeseen at first, the notion admits beautiful and exotic examples some of
which appeared earlier in diverse contexts. Squarelike groups were invented by
the authors in a previous paper and may be viewed as nonstandard discriminating
groups. In this paper we give examples of groups which are discriminating or
squarelike as well as groups which are not. The main result is the existence of
a finitely generated squarelike group which is not discriminating.

** Charles Megibben,** Department of Mathematics, Vanderbilt University,
Nashville Tennessee 37240 (charles.k.megibben@vanderbilt.edu) and **
William Ullery,**
Department of Mathematics, Auburn University, Auburn, Alabama 36849
(ullery@math.auburn.edu).

On global abelian k-groups,
pp. 675-692.

ABSTRACT.
The class of global *k*-groups is an abundant class of abelian groups that
contains, but is not restricted to, all torsion groups, torsion-free separable
groups, and mixed groups with decomposition bases. Our main theorem is that a
global
*k*-group of cardinality À_{n} (for
some nonnegative integer n)* *has sequentially pure projective dimension at
most n. This was known previously only in the special case where n≤1

**Luigi Salce, ** Dipartimento di Matematica Pura e Applicata, Università
di Padova, Italy (salce@math.unipd.it).

On the Minimal Injective Cogenerator
over Almost Perfect Domains,
pp. 693-705.

ABSTRACT.
Let *R* be a local almost perfect domain with maximal ideal *P*. The
minimal injective cogenerator E(*R*/*P*) and its endomorphism ring *
A* are investigated. It is shown that, if *R* is non-Noetherian and the
square of *P* is open in the Prüfer (i.e., finitely embedded) topology,
then *A* strictly contains the completion of *R*, which coincides with
its center, hence *A* is non-commutative. The new class of
*P*-chained domains is introduced. These rings are local almost perfect and
pseudo-valuation domains. It is proved that in the Noetherian case they coincide
with the pseudo-valuation domains, and in the non-Noetherian case they satisfy
the condition which ensures that the ring
* A* is non-commutative.

**Mohammad Saleh**, Mathematics Department, Birzeit University, West Bank,
Palestine, (msaleh@birzeit.edu).

Serre class and the direct sums of
modules,
pp. 707-720.

ABSTRACT.
The purpose of this paper is to further the study of weakly injective and weakly
tight modules a generalization of injective modules. For a Serre class K of
modules, we study when direct sums of modules from K satisfies a property P in
K. In particular, we get characterization of locally q.f.d. modules in terms of
weak tightness.

**Kazuhiro Ichihara, ** Nara Women's University, Nara 630-8506, Japan (ichihara@vivaldi.ics.nara-wu.ac.jp)
and ** Shin Satoh,** Chiba University, Chiba 263-8522, Japan (satoh@math.s.chiba-u.ac.jp).

Liftability for double coverings
of immersions of non-orientable surfaces into 3-space, pp. 721-741.

ABSTRACT.
We prove that the double covering map of any generic immersion of a projective
plane into 3-space does not lift to an embedding into 4-space. To prove this, we
give a criterion of the liftability for double coverings of immersions of any
non-orientable surfaces.

**Bang-Yen Chen, ** Department of Mathematics, Michigan State University,
East Lansing, MI 48824--1027, USA (bychen@math.msu.edu) and **Ion Mihai,**
Faculty of Mathematics, University of Bucharest, Str. Academiei 14,70109
Bucharest, Romania (imihai@math.math.unibuc.ro).

Isometric Immersions of contact
Riemannian Manifolds in real space forms, pp. 743-764.

ABSTRACT.
In this paper we define some contact Riemannian invariants for almost contact
metric manifolds which are analogues to those invariants originally defined for
general Riemannian manifolds introduced by the first author. We then establish
sharp inequalities between these contact Riemannian invariants and the squared
mean curvature for almost contact Riemannian manifolds in a Riemannian manifold
of constant curvature. We also investigate almost contact Riemannian
submanifolds which verify the equality case of the inequalities. Moreover,
examples of contact Riemannian submanifolds satisfying the equality case are
provided as well.

**Changrim Jang, ** Mathematics Department, Wichita State University, Wichita
KS 67260-0033, USA (crjang@mail.ulsan.ac.kr) (permanent address: Department of
Mathematics, College of Natural Sciences, University of Ulsan, Ulsan 680-749,
Republic of Korea), **Phillip E.** **Parker,** Mathematics Department,
Wichita State University, Wichita KS 67260-0033, USA (phil@math.wichita.edu)
(http://www.math.wichita.edu/~pparker/), and **Keun ****Park, **
Department of Mathematics, College of Natural Sciences, University of Ulsan,
Ulsan 680-749, Republic of Korea (kpark@mail.ulsan.ac.kr}.

Pseudo *H*-type 2-step
Nilpotent Lie Groups, pp. 765-786.

ABSTRACT.
Pseudo *H*-type is a natural generalization of *H*-type to geometries
with indefinite metric tensors. We give a complete determination of the
conjugate locus including multiplicities. We also obtain a partial
characterization in terms of the abundance of totally geodesic, 3-dimensional
submanifolds.

**Ivansic, Ivan, **
Department of Mathematics, University of Zagreb, Unska 3, P.O. Box 148, 10001
Zagreb, Croatia
(ivan.ivansic@fer.hr),
and **Rubin, Leonard R., **
Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA
(lrubin@ou.edu).

Limit Theorem for
Semi-sequences in Extension Theory, pp. 787-807.

ABSTRACT.
Given an inverse sequence **X** = (X_{i},p_{i}^{i+1})
of topological spaces along with subspaces T_{i} of X_{i}
and an infinite subset N* of the set of positive integers N, we define the
concept of a semi-sequence **T**=(T_{i},N*) and its semi-limit
T=semi-lim **T** which is a subset of X=lim **X**. A notion of stability
of **T** in **X** is defined along with extendability of
**X** with respect to a given CW-complex K and **T**. We show that if the
terms X_{i} of the inverse sequence are stratifiable, T_{i} is
closed in X_{i}, and stability and extendability apply, then K is an
absolute extensor for T. All previous extension theoretic limit theorems about
inverse sequences are corollaries to this result.

**Yan-Kui Song, **Department of Mathematics, Nanjing Normal
University, Nanjing 210097, China (songyankui@njnu.edu.cn).

Conditions which imply
Lindelöfness in star-Lindelöf spaces, pp. 809-813.

ABSTRACT.
In this paper we prove that every regular star-Lindelöf space is Lindelöf if
and only if every increasing open cover U_{α}, α< τ, admits an
increasing open cover V_{α} such that the closures of the V_{α}
are contained in the U_{α}.

**Bonami, Aline** Université d'Orléans, BP 6759, F 45067 Orléans Cédex 2,
France (aline.bonami@univ-orleans.fr) and **Luo Luo, ** Department
of Mathematics, University of Science and Technology of China, Hefei, Anhui
230026, P. R. China (lluo@ustc.edu.cn).

On Hankel Operators between Bergman
Spaces on the Unit Ball, pp. 815-828.

ABSTRACT.
We study the boundedness of a (small) Hankel operator between different Bergman
spaces on the unit ball B in C^{n}. We give conditions on its symbol
which are necessary and/or sufficient for the continuity of the corresponding
operator from A^{p}(B) into A^{q}(B), for all finite p,q >0.

**Kenneth J. Dykema** and **Roger R. Smith, ** Department of
Mathematics, Texas A&M University, College Station TX 77843--3368, USA
(kdykema@math.tamu.edu), (rsmith@math.tamu.edu).

The completely bounded approximation
property for extended Cuntz--Pimsner algebras, pp. 829-840.

ABSTRACT.
The extended Cuntz-Pimsner algebra E(H), introduced by Pimsner, is constructed
from a Hilbert B,B-bimodule H over a C*-algebra B. In this paper we investigate
the Haagerup Lambda invariant for these algebras, the main result being that the
value of this invariant for E(H) equals that for B whenever H is full over B. In
particular, E(H) has the completely bounded approximation property if and only
if the same is true for B.

**D.E. Edmunds,** Department of Mathematics, University of Sussex, Falmer,
Brighton, BN1 9RF, UK (D.E.Edmunds@sussex.ac.uk) and **E. Shargorodsky, **
{Department of Mathematics, King's College London, Strand, London, WC2R 2LS, UK}
(eugene.shargorodsky@kcl.ac.uk)

The inner variation of an operator and the essential norms of pointwise
multipliers in function spaces, pp. 841-855.

ABSTRACT.
We show that useful estimates for the essential norm of pointwise multipliers
acting on a function space may be easily obtained from certain
functional-analytic facts related to the notions of inner variation and the
measure of noncompactness. Applications to Besov and Lizorkin-Triebel spaces are
given.

**Zhiguo Hu, ** University of Windsor, Windsor, Ontario, N9B 3P4, Canada
(zhiguohu@uwindsor.ca).

Maximally Decomposable von Neumann
Algebras on Locally Compact Groups and Duality, pp. 857-881.

ABSTRACT.
We present a decomposition of the abelian von Neumann algebra L_{∞}(G)
of a locally compact group as an inductive union of certain maximally
decomposable translation invariant sub von Neumann algebras. As an application
of the decomposition, for all locally compact groups G, we precisely express the
weight and the cardinality of the spectrum of L_{∞}(G) in terms of the
character and the compact covering number of G. Using decomposability numbers of
von Neumann algebras, we provide a unified formulation of the decomposition of L_{∞}(G)
and its dual version on VN(G) in the setting of Kac algebras. A concept of
Kakutani-Kodaira numbers for locally compact groups and general Kac algebras is
introduced. It is used to reveal some quantitative intrinsic relations between L_{∞}(G),
VN(G) and the underlying group G. A Kac algebraic Kakutani-Kodaira theorem on
the dual pair L_{∞}(G) and VN(G) is obtained.

**Pawel Kolwicz, **Institute of Mathematics, University of Technology, ul.
Piotrowo 3a, 60-965 Poznañ, Poland (
kolwicz@math.put.poznan.pl ) .

Rotundity properties in
Calderón-Lozanovskií spaces, pp. 883-912.

ABSTRACT.
We find criteria for strict and uniform convexity of Calderón-Lozanovskií spaces
solving problem XII from [3] and generalizing several theorems, which give only
the sufficient (or necessity) conditions (see [2], [4]). In particular we obtain
the respective criteria for Orlicz-Lorentz spaces which has been proved directly
in [1], [5], [6]. We give also applications to Orlicz spaces generated by the
composing of Orlicz functions.

*References: ***[1]** J. Cerdá, H. Hudzik, A. Kamiñska and M.
Mastylo, * Geometric properties of symmetric spaces with applications to
Orlicz-Lorentz spaces *, Positivity 2 (1998), 311-337.
**[2]** J. Cerdá, H. Hudzik and M. Mastylo, *On the geometry of some
Calderón-Lozanovskií interpolation spaces*, Indag. Math. N.S. 6(1), (1995),
35-49.
**[3]** S. Chen, Y. Cui, H. Hudzik and T. Wang, *On some solved and
unsolved problems in geometry of certain classes of Banach function spaces*,
Unsolved Problems on Mathematics for the 21st Century, J. M. Abe and Tanaka
(Eds.) IOS Press, 2001. **[4]** H. Hudzik, A. Kamiñska and M. Mastylo, *
Geometric properties of some Calderón-Lozanovskií spaces and Orlicz-Lorentz
spaces*, Houston J. Math. 22(3), (1996), 639-663.
**[5]** A. Kamiñska, *Some remarks on Orlicz-Lorentz spaces*, Math.
Nachr. 147, (1990), 29-38.
**[6]** A. Kamiñska, *Uniform convexity of generalized Lorentz spaces*,
Arch. Math. 56 (1991), 181-188.

**Guyan Robertson, ** School of Mathematics and Statistics, University of
Newcastle, NE1 7RU, U.K.} (a.g.robertson@newcastle.ac.uk).

Boundary operator algebras for
free uniform tree lattices, pp. 913-935.

ABSTRACT.
Let X be a finite connected graph, each of whose vertices has degree at least
three. The fundamental group of X is a free group which acts on the boundary of
the universal covering tree, endowed with a natural topology and Borel measure.
The corresponding crossed product C*-algebra depends only on the rank of the
free group and is a Cuntz-Krieger algebra whose structure is explicitly
determined. The crossed product von Neumann algebra does not possess this
rigidity. If the tree is homogeneous then the von Neumann algebra is a purely
infinite hyperfinite factor whose exact type depends on whether X is bipartite
or not.

**Zhong, Hualiang,** Robarts Research Institute, London, Ontario, Canada
N6A 5K8 (hzhong@imaging.robarts.ca) and **Boivin, André,** University of
Western Ontario, London, Ontario, Canada N6A 5B7 (boivin@uwo.ca).

On a class of non-harmonic
Fourier series, pp. 937-956.

ABSTRACT.
In the theory of non-harmonic Fourier series, one-quarter theorems deal with
basis, frames and/or series expansion properties under some extreme conditions.
In this paper we show the existence of a series representation analogous to the
Fourier series for square integrable functions in terms of system of complex
exponentials when the sequence of exponents is close to the "extreme case"
sequence {n+sign(n)¼}.

**S. Eidelman,** Department of Mathematics, International
Solomon University, Sheludenko 1b, Kiev, Ukraine, and **Y. Eidelman, **
School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv
University, Ramat-Aviv 69978, Israel (eideyu@post.tau.ac.il).

On regularity of the extremal
solution of the Dirichlet problem for some semilinear elliptic equations of the
second order, pp. 957-960.

ABSTRACT.
We consider the problem on the regularity of the extremal positive solution of
the Dirichlet problem for superlinear elliptic equations with a positive
parameter. We prove the smoothness of the extremal solution for a certain class
of nonlinearities. In this class we distinguish a subclass of functions for
which the extremal solution is classical in the space of any dimension.

**Zhaoyang Yin, **Department of Mathematics, Zhongshan
University, 510275 Guangzhou, China (mcsyzy@zsu.edu.cn).

Well-posedness and blowup
phenomena for a class of nonlinear third-order partial differential equations,
pp. 961-972.

ABSTRACT.
We establish the local well-posedness for a class of nonlinear third-order
partial differential equations. We also present a blow up scenario and prove
that the equation has strong solutions that blow up in finite time.