*Editors*: D. Bao (San Francisco, SFSU), D. Blecher
(Houston), B. 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 Editors*: B. G. Bodmann and K. Kaiser (Houston)

Houston Journal of Mathematics

*Contents*

Gábor Braun,
Industrial and Systems Engineering, Georgia Institute of Technlogy, 755 Ferst
Drive, NW, Atlanta, GA 30332, USA
gabor.braun@isye.gatech.edu
and
Lutz Strüngmann,
Faculty for Computer Sciences, University of Applied Sciences Mannheim, 68163
Mannheim, Germany
l.struengmann@hs-mannheim.de
.

Examples of non-dual subgroups of the Baer-Specker group, pp. 723-739.

ABSTRACT. In this note we prove three results concerning dual groups of
subgroups of the Baer-Specker group. Firstly, we construct one of size
2^{ℵ0}, which is not a dual group, and hence
strongly non-reflexive. In contrast, due
to [Göbel
and Pokutta, Construction of dual modules using Martin's axiom,
J. Algebra 320 (2008), no. 6, 2388-2404], under Martin-s axiom
every subgroup strictly smaller than the continuum is actually a dual
group. Secondly, we show that the latter is not a theorem of ZFC, as
adding ℵ_{1} many Cohen reals to the ground model, we obtain a
model of ZFC in which there is a non-dual subgroup of size ℵ_{1}.
However, the continuum may be large. Thirdly, we
construct using Martin's axiom a subgroup whose nth dual is not an (n
+ 1)st dual for any n. Together our results solve two questions from
the book
by [Eklof
and Mekler, Almost free modules, North-Holland Mathematical Library,
vol. 65, North-Holland Publishing Co., Amsterdam, 2002].

**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)
.

On the preservation of the standard characterizations of some colimits in the
passage from single-sorted to many-sorted universal algebra, pp. 741-760.

ABSTRACT. This article addresses the question: For which families of many-sorted algebras are the standard characterizations of the directed colimits, reduced products, and ultraproducts of single-sorted algebras preserved? By defining, for a fixed many-sorted signature, the concept of family of many-sorted algebras with constant support we extend to many-sorted universal algebra the standard characterizations, i.e., those made by means of the so-called eventually consistent choice functions, of the aforementioned colimits of single-sorted universal algebra; thus giving an answer to the question posed at the beginning. Moreover, we state the characterizations of the quasiequationalclasses and of the finitary quasiequational classes of many-sorted algebras, both due to G. Matthiessen (but not as well known as they really deserve to be), showing, in particular, that for the former the concept of family with constant support is essential.

**Jun Li**, School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China (yysxlj@163.com), **
Di-Ming Lu**, School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China(dmlu@zju.edu.cn).

Higher Koszul duality for piecewise-Koszul algebras, pp. 761-773.

ABSTRACT. The piecewise-Koszul algebras are generalizations of classical Koszul and higher Koszul algebras. We give a criterion for a connected graded algebra A to be a piecewise-Koszul algebra in terms of an A-infinity algebra structure on its Koszul dual.

**Liu Yang, **
Department of Mathematics,
East China Normal University, Shanghai 200241, P.R.China
yangliu20062006@126.com,
**Xiaojun Liu,**Department of Mathematics,
University of Shanghai for Science and Technology, Shanghai 200093, P.R.China.
xiaojunliu2007@hotmail.com and
**Xuecheng Pang, **Department of Mathematics,
East China Normal University, Shanghai 200241, P.R.China
xcpang@math.ecnu.edu.cn.

On families of meromorphic maps into the complex projective space, pp. 775-789.

ABSTRACT. This paper is devoted to study normality criteria for families of holomorphic
mappings of several complex variables into an arbitrary closed set in P^{N}(C), rather than just the projective space.
And our results improve some earlier work.
As applications, some meromorphic normality criteria for families of meromorphic
mappings are given.

Some notes on pluriregular condensers, pp. 791-802.

ABSTRACT. In his paper,

Subsets of the variety X⊂ P

**Adam Osękowski,**
Department of Mathematics, Informatics and Mechanics, University of Warsaw, 02-097 Warsaw, Poland
(ados@mimuw.edu.pl

Sharp inequalities for monotone bases in L^{1}, pp. 833-851.

ABSTRACT. We introduce a novel method which can be used to establish general sharp maximal inequalities for monotone bases and contractive projections in
L^{1}. The technique enables to deduce such estimates from the existence of the upper solutions to the corresponding nonlinear problems. As an application, we identify the best unconditional-type constants in certain maximal and weak-type inequalities for monotone bases in
L^{1}.

**Casazza, Peter G.,**
University of Missouri-Columbia, MO 65201
(casazzap@missouri.edu), **Lynch, Richard G.,** University of Missouri-Columbia, MO 65201
(rglz82@mail.missouri.edu),
**Tremain, Janet, **University of Missouri-Columbia, MO 65201
(tremainjc@missouri.edu), Woodland, Lindsey M., University of Missouri-Columbia, MO 65201
(lindsey.woodland@prognosinc.com).

Integer Frames, pp. 853-875.

ABSTRACT. Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed orthonormal basis for a Hilbert space. Integer frames have potential to mitigate quantization errors and transmission losses as well as speeding up computation times. This paper gives the first systematic study of this important class of finite Hilbert space frames.

**Flavia Colonna**
Department of Mathematical Sciences, College of Science, George Mason University, 4400 University Drive, Fairfax, Virginia, 22030, U.S.A.
(fcolonna@gmu.edu) and **Maria Tjani
**Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas, 72701, U.S.A.
(mtjani@uark.edu)
Essential norms of weighted composition operators from reproducing kernel Hilbert spaces into weighted-type spaces, pp. 877-903.

ABSTRACT. In this work, we study weighted composition operators acting on a reproducing kernel Hilbert space of analytic functions and mapping into a weighted-type Banach space or a Bloch-type space. Our main result is an approximation of the essential norm of such operators. Moreover, we obtain an exact formula for the operator norm and the essential norm when the operator maps certain weighted Hardy spaces, including the Hardy Hilbert space, the Bergman Hilbert space, and the logarithmic Bergman Hilbert space into a weighted-type Banach space.

**Azin Golbaharan** and **Hakimeh Mahyar**,
Department of Mathematics, Kharazmi University, 15618, Tehran Iran
(golbaharan_azin@yahoo.com),
(golbaharan@khu.ac.ir),
(mahyar@khu.ac.ir).

Weighted composition operators on Lipschitz algebras, pp. 905-917.

ABSTRACT. We provide a complete
description of weighted composition operators on Lipschitz
algebras. We also give necessary and sufficient
conditions for the injectivity and the surjectivity of these
operators. Then we establish a necessary and sufficient condition
for a weighted composition operator on Lipschitz algebras to be compact.
Finally, we obtain a lower bound for the essential norms of
weighted composition operators on the Lipschitz algebra.

Analytic free semigroup algebras and Hopf algebras , pp. 919-943.

ABSTRACT. In this paper, we explore richer structures of an analytic free semigroup algebra and its predual. We prove that both are Hopf algebras. Moreover, their structures are closely connected with each other: There is a bijection between the set of corepresentations of an analytic free semigroup algebra and the set of completely bounded representations of its predual on one hand; and an analytic free semigroup algebra can be recovered from the coefficient operators of completely bounded representations of its predual on the other hand. As an amusing application of our results, the (Gelfand) spectrum of the predual is identified. Surprisingly, the main results of this paper seem new even in the classical case.

Bustos, Harold, Facultad de Ciencias, Universidad de Chile, Santiago, Chile and

C*-Algebraic Covariant Structures, pp. 945-975.

ABSTRACT. We introduce

K. Li

Characterization of a Two Weight Inequality for Multilinear Fractional Maximal Operators, pp. 977-990.

ABSTRACT. In this paper, we study the characterization of two weight inequality for multilinear fractional maximal operators and extend Sawyer's two weight testing condition to the multilinear case. For certain Lebesgue space indices, we show that the boundedness of the multilinear fractional maximal operators is equivalent to the multilinear version of Sawyer type testing condition. And for general indices, we also provide a characterization.

**Catalin Dragan**, Department of Mathematics, University of Cincinnati, P. O.
Box 210025 Cincinnati, OH, 45221-0025, USA,
dragancn@mail.uc.edu and **Victor Kaftal**, Department of Mathematics, University of Cincinnati, P. O. Box 210025 Cincinnati,
OH, 45221-0025, USA, victor.kaftal@uc.edu.

Sums of equivalent sequences of positive operators in von Neumann factors, pp. 991-1017.

ABSTRACT. Let *A* be a positive operator in an infinite, σ-finite von Neumann factor Μ and
let {*B*_{j}} a sequence in Μ^{+}.
We give sufficient conditions for the decomposition
*A*=∑_{j=1}^{∞} *C*_{j}
to hold when *C*_{j} is equivalent to *B*_{j} for all *j*
(where *C* equivalent to *B* means *C*=*XX*^{*} and
*B*=*X*^{*}*X* for some *X* in Μ)
and when *C*_{j} are unitarily equivalent to *B*_{j} for
all *j*.

**Aurichi, Leandro F**.**,** Instituto de Ciências Matemáticas e de Computação (ICMC-USP), Universidade de São Paulo, São Carlos, SP - CEP 13566-590 - Brazil
(aurichi@icmc.usp.br), and ** Mezabarba, Renan M.,** Instituto de Ciências Matemáticas e de Computação (ICMC-USP), Universidade de São Paulo, São Carlos, SP - CEP 13566-590 - Brazil
(rmmeza@icmc.usp.br).

Productively countably tight spaces of the form C_{k}(X),
pp. 1019-1029.

ABSTRACT. Let X be a Tychonoff space and consider its hyperspace C_{p}(X), the space of the continuous real functions on X with the topology of the pointwise convergence. In this paper, with the use of bornologies, we generalize some results concerning convergence properties of C_{p}(X) for a class of topologies on C(X), that includes the pointwise converngence topology as well as the compact open topology. In particular, we obtain necessary and sufficient conditions to the space C(X) to be productively countably tight with the compact open topology.

**Morgan, Charles J. G.,** Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK, and Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Avenida Professor Gama Pinto, 2, 1649-003, Lisboa, Portugal
(charles.morgan@ucl.ac.uk) and
**da Silva, Samuel G.,** Instituto de Matemática, Universidade Federal da Bahia, Campus de Ondina, Av. Adhemar de Barros, S/N, Ondina, CEP 40170-110, Salvador, BA, Brazil
(samuel@ufba.br)..

Selectively (a)-spaces from almost disjoint families are necessarily countable under a certain parametrized weak diamond principle, pp.
1031-1046.

ABSTRACT.he second author has recently shown that any selectively (a) almost disjoint family must have cardinality strictly less than 2^{ℵ0}, so under the Continuum Hypothesis such a family is necessarily countable. However, it was also shown by the same author that 2^{ℵ0} < 2^{ℵ1} alone does not avoid the existence of uncountable selectively (a) almost disjoint families. We show in this paper that a certain effective parametrized weak diamond principle is enough to ensure countability of the almost disjoint family in this context. We also discuss the deductive strength of this specific weak diamond principle (which is consistent with the negation of the Continuum Hypothesis, apart from other features).

**Juan L.G. Guirao,** Departamento de Matemática Aplicada y Estadística. Universidad Politécnica de Cartagena, Hospital de Marina, 30203–Cartagena, Regíon de Murcia, Spain
(juan.garcia@upct.es),
**Jaume Llibre,** Departament de Matemátiques, Universitat Autònoma de Barcelona, Bellaterra, 08193–Barcelona, Catalonia
(jllibre@mat.uab.cat.

Periods of homeomorphisms on some compact spaces, pp. 1047-1058.

ABSTRACT. The objective of the present paper is to provide information on the set of periodic points of a homeomorphism deﬁned in the following compact spaces: S^{n}
(the n– dimensional sphere), S^{n×m }the product space of the n–dimensional with the m– dimensional spheres), CP^{n } the n–dimensional complex projective space) and HP^{n }(the n–dimensional quaternion projective space). We use as main tool the action of the homeomorphism on the homology groups of these compact spaces.

**Shou Lin**, Institute of Mathematics, Ningde Normal University,
Ningde 352100, P. R. China, Department of Mathematics, Minnan Normal University,
Zhangzhou 363000, P.R. China
(shoulin60@163.com), and
**Zhangyong Cai**, Department of Mathematics, Guangxi Teachers Education University, Nanning 530023, P.R. China.

Closed mappings, boundary-compact mappings and sequence-covering mappings, pp. 1059-1078

ABSTRACT. Yoshio Tanaka and Chuan Liu posed the following question in 1999: Let f be a closed mapping from X to Y. Under what conditions on X or Y,
does the boundary of the fiber of every point in Y have some nice properties?
In this paper, the following two related questions are discussed.
(1) When is a closed mapping to be a boundary-compact mapping or boundary-Lindelöf mapping?
(2) When is a sequence-covering boundary-compact mapping or boundary-Lindelöf mapping to be a 1-sequence-covering mapping?
The following results on generalized metric spaces are obtained, which answers a few questions in literature.
(a) Suppose that f is a closed mapping from X to Y, where X is a regular k-space with a point-countable k-network or a regular sequential space with a point-countable w-system.
If Y contains no closed copy of Sω, then f is a boundary-compact mapping.
(b) Suppose that f is a closed mapping from X to Y, where X is a k*-metrizable k-space.
If Y contains no closed copy of Sω_{1}, then f is a boundary-s-mapping.
(c) Suppose that f is a sequence-covering boundary-compact mapping from X to Y.
If X is first-countable, then f is a 1-sequence-covering mapping.
(d) Suppose that f is a sequence-covering boundary-Lindelöf mapping from X to Y,
where X is first-countable. Then Y is snf-countable if and only if f is a 1-sequence-covering mapping.