Continuous Semigroups in Banach Algebras

by Allan M. Sinclair

Overview

In these notes the abstract theory of analytic one-parameter semigroups in Banach algebras is discussed, with the Gaussian, Poisson and fractional integral semigroups in convolution Banach algebras serving as motivating examples. Such semigroups are constructed in a Banach algebra with a bounded approximate identity. Growth restrictions on the semigroup are linked to the structure of the underlying Banach algebra. The Hille-Yosida Theorem and a result of J. Esterle's on the nilpotency of semigroups are proved in detail. The lecture notes are an expanded version of lectures given by the author at the University of Edinburgh in 1980 and can be used as a text for a graduate course in functional analysis.

Product Details

ISBN-13:	9780521285988
Publisher:	Cambridge University Press
Publication date:	06/17/1982
Series:	London Mathematical Society Lecture Note Series , #63
Pages:	152
Product dimensions:	5.98(w) x 8.98(h) x 0.35(d)

Table of Contents

1. Introduction and preliminaries; 2. Analytic semigroups in particular Banach algebras; 3. Existence of analytic semigroups - an extension of Cohen's factorization method; 4. Proof of the existence of analytic semigroups; 5. Restrictions on the growth of at; 6. Nilpotent semigroups and proper closed ideals; Appendix 1. The Ahlfors-Heins theorem; Appendix 2. Allan's theorem - closed ideals in L1( R+,w); Appendix 3. Quasicentral bounded approximate identities; References; Index.