Title
Algebras of Continuous Functions: Frechet Function Algebras, QAlgebras and Automatic Continuity,Used
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This book covers some aspects of the theory of Topological algebras including Frechet algebras and Qalgebras. 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 kspace is of exponential type under certain conditions. Using this result, we generalize the ArensRoyden 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 kspaces 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 Qalgebra, are all equivalent. Then it is shown that every homomorphism from a Qalgebra 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
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