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The Trace in Banach Jordan Pairs
Author(s) -
Hessenberger Gerald
Publication year - 1998
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609398004627
Subject(s) - mathematics , trace (psycholinguistics) , bounded function , pure mathematics , algebraic number , mathematical analysis , philosophy , linguistics
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. 1991 Mathematics Subject Classification 17C65, 46H70.