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LAP Lambert Academic Publishing Algebras of Continuous Functions: Frechet Function Algebras, Q-Algebras and Automatic Continuity

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Description

This book covers some aspects of the theory of Topological algebras including Frechet algebras and Q-algebras. It is devided into three chapters. In the first chapter, the basic concepts necessary for the understanding of the subject matter are introduced. In chapter 2 we show that a continuous function on a hemicompact k-space is of exponential type under certain conditions. Using this result, we generalize the Arens-Royden Theorem to Frechet algebras and obtain interesting results on the density of invertible elements in uniform Frechet algebras. We also find a topological condition to characterize hemicompact k-spaces on which every continuous function has square root. In chapter 3 we show that in a topological algebra, the upper semicontinuity of the spectrum function, the upper semicontinuity of the spectral radius function, the continuity of the spectral radius function at zero, and being a Q-algebra, are all equivalent. Then it is shown that every homomorphism from a Q-algebra with a complete metrizable topology onto a semisimple Frechet algebra is automatically continuous. Also we get some results on the continuity of homomorphisms between regular Frechet algebras

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
02 July 2012
Listed Since
06 July 2012

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