Spectral properties of locally holomorphic vector-valued functions

Harm Bart
1974 Pacific Journal of Mathematics  
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
more » ... a correctly stated but incorrectly proven theorem of L. Mittenthal.
doi:10.2140/pjm.1974.52.321 fatcat:n4shvb6qhrgzxgjn4wdltk7umu