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Spectral properties of
locally holomorphic vector-valued functions
Harm Bart |
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Vol. 52 (1974), No. 2, 321–329
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Abstract |
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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
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Milestones
Received: 1 December 1972
Published: 1 June 1974
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Authors |
| Harm Bart | |
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