Vol. 66, No. 2, 1976

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ISSN: 0030-8730
The spectra of endomorphisms of algebras of analytic functions

Herbert Meyer Kamowitz

Vol. 66 (1976), No. 2, 433–442
Abstract

Suppose 0 < R < 1, G is the open annulus {zR < |z| < 1} and A(G) denotes the uniform algebra of functions analytic on G and continuous on G. Each nonzero endomorphism T of A(G) has the form Tf = f φ for some φ A(G) with φ(G) G. In the main result of this note, the spectra of endomorphisms of A(G) are determined for the case where the inducing maps φ have a fixed point in G. In addition, further results are discussed for other algebras of analytic functions.

Mathematical Subject Classification 2000
Primary: 47B37
Secondary: 46J15
Milestones
Received: 10 May 1976
Published: 1 October 1976
Authors
Herbert Meyer Kamowitz