Algebra homomorphisms and the functional calculus

Mark Phillip Thomas

Vol. 79 (1978), No. 1, 251–269

DOI: 10.2140/pjm.1978.79.251

Abstract

Let b be a fixed element of a commutative Banach algebra with unit. Suppose σ(b) has at most countably many connected components. We give necessary and sufficient conditions for b to possess a discontinuous functional calculus.

Mathematical Subject Classification 2000

Primary: 46J05

Secondary: 46H30

Milestones

Received: 22 November 1976

Published: 1 November 1978