Continuous semigroups in Banach algebras / Allan M. Sinclair.

Format:

Book

Author/Creator:

Sinclair, Allan M., author.

Series:

London Mathematical Society lecture note series ; 63.

London Mathematical Society lecture note series ; 63

Language:

English

Subjects (All):

Banach algebras.

Semigroups.

Physical Description:

1 online resource (145 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1982.

Language Note:

English

Summary:

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.

Contents:

Cover; Title; Copyright; 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 NILPOTEMT SEMIGROUPS AND PROPER CLOSED IDEALS; APPENDIX 1 : THE AHLFORS-HEINS THEOREM; APPENDIX 2: ALLAN'S THEOREM - CLOSED IDEALS IN L1(R+, ω); APPENDIX 3: QUASICENTRAL BOUNDED APPROXIMATE IDENTITIES; REFERENCES; INDEX

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Inludes bibliographical references and index.

ISBN:

1-139-88406-9

1-107-36607-0

1-107-37080-9

1-107-36116-8

1-107-36990-8

1-299-40387-5

1-107-36361-6

0-511-66242-4