Vol. 52, No. 2, 1974

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ISSN: 0030-8730
Spectral properties of locally holomorphic vector-valued functions

Harm Bart

Vol. 52 (1974), No. 2, 321–329
Abstract

This paper deals with spectral properties of commutative locally holomorphic Banach algebra valued functions. One of the main concepts is that of a spectral set of such a function. This concept, which is due to L. Mittenthal, extends that of a spectral set of a single Banach algebra element. It will be shown that the spectral idempotent associated with a nonvoid spectral set is nonzero. This result is a generalization of a well-known theorem in ordinary spectral theory. It will be used to prove a correctly stated but incorrectly proven theorem of L. Mittenthal.

Mathematical Subject Classification 2000
Primary: 46H05
Secondary: 47A60
Milestones
Received: 1 December 1972
Published: 1 June 1974
Authors
Harm Bart