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.

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: Sⁿ (the n– dimensional sphere), S^n×m the product space of the n–dimensional with the m– dimensional spheres), CPⁿ the n–dimensional complex projective space) and HPⁿ (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 Sω₁, 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.