Abstract
For certain m-tuples $a = {a_1, ... ,a_n)$ of elements $a_j$ in a unital Ba11ach algebra, we construct a joint spectrum $\gamma(a)$ and a functional calculus with a spectral mapping theorem. It is not assumed that the $a_j$ j commute but rather that they commute modulo the Jacobson radical of the algebra they generate. For matrices, this last condition is equivalent to their being simultaneously triangularizable. This work extends that of M.E. Taylor, R.F.V. Anderson, and A. Mcintosh and A. Pryde.
Information
Published: 1 January 1988
First available in Project Euclid: 18 November 2014
zbMATH: 0705.47013
MathSciNet: MR1009602
Rights: Copyright © 1988, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.
