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THE TRACE IN BANACH JORDAN PAIRS

Published online by Cambridge University Press:  01 November 1998

GERALD HESSENBERGER
GERALD HESSENBERGER
Affiliation:
Institut für Mathematik, Universität Innsbruck, Technikerstrasse 25/7, A-6020 Innsbruck, Austria
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Abstract

The algebraic trace form (as defined by O. Loos) of an element (x, y) of a (complex) Banach Jordan pair V, where x or y is in the socle, is equal to the sum of the products of all spectral values and their multiplicity. The trace form is calculated for two examples, the Banach Jordan pair of bounded linear operators between two Banach spaces, and the Banach Jordan pair of a quadratic form. Using analytic multifunctions, it is also shown that the complement of the socle of a Banach Jordan pair V is either dense or empty. In the last case, V has finite capacity.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 6 , November 1998 , pp. 561 - 568
Copyright
© The London Mathematical Society 1998

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