Vol. 52, No. 2, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Spectral properties of locally holomorphic vector-valued functions

Harm Bart

Vol. 52 (1974), No. 2, 321–329

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
Received: 1 December 1972
Published: 1 June 1974
Harm Bart