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Journal of Function Spaces
Volume 2015, Article ID 850709, 6 pages
http://dx.doi.org/10.1155/2015/850709
Research Article

Topological and Functional Properties of Some -Algebras of Holomorphic Functions

Maritime Faculty, University of Montenegro, Dobrota 36, 85330 Kotor, Montenegro

Received 16 June 2015; Accepted 26 August 2015

Academic Editor: Alberto Fiorenza

Copyright © 2015 Romeo Meštrović. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let    be the Privalov class of holomorphic functions on the open unit disk in the complex plane. The space equipped with the topology given by the metric defined by , , becomes an -algebra. For each , we also consider the countably normed Fréchet algebra of holomorphic functions on which is the Fréchet envelope of the space . Notice that the spaces and have the same topological duals. In this paper, we give a characterization of bounded subsets of the spaces and weakly bounded subsets of the spaces with . If denotes the strong dual space of and denotes the space of complex sequences satisfying the condition , equipped with the topology of uniform convergence on weakly bounded subsets of , then we prove that both set theoretically and topologically. We prove that for each    is a Montel space and that both spaces and are reflexive.