Proceedings of the Centre for Mathematics and its Applications

A non-commutative joint spectral theory

A. J. Pryde

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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.

Article information

Source
Workshop/Miniconference on Functional Analysis and Optimization. Simon Fitzpatrick and John Giles, eds. Proceedings of the Centre for Mathematical Analysis, v. 20. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1988), 153-161

Dates
First available in Project Euclid: 18 November 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1416340111

Mathematical Reviews number (MathSciNet)
MR1009602

Zentralblatt MATH identifier
0705.47013

Citation

Pryde, A. J. A non-commutative joint spectral theory. Workshop/Miniconference on Functional Analysis and Optimization, 153--161, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1988. https://projecteuclid.org/euclid.pcma/1416340111


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