Vol. 79, No. 1, 1978

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Algebra homomorphisms and the functional calculus

Mark Phillip Thomas

Vol. 79 (1978), No. 1, 251–269
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
Authors
Mark Phillip Thomas