Compact endomorphisms of Banach algebras

Herbert Meyer Kamowitz

Vol. 89 (1980), No. 2, 313–325

DOI: 10.2140/pjm.1980.89.313

Abstract

Let T be a compact endomorphism of a commutative semi-simple Banach algebra B. This paper discusses the behavior of the adjoint T^∗ of T on the set X′ of multiplicative linear functionals on B. In particular it is shown that ∩T^∗n(X′) is finite, thus generalizing the example of compact endomorphisms of the disc algebra.

Mathematical Subject Classification 2000

Primary: 46J05

Secondary: 46J10

Milestones

Received: 12 September 1979

Revised: 29 November 1979

Published: 1 August 1980