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A JORDAN-LIKE DECOMPOSITION IN THE NONCOMMUTATIVE SCHWARTZ SPACE

Part of: Topological (rings and) algebras with an involution Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  15 December 2014

KRZYSZTOF PISZCZEK
KRZYSZTOF PISZCZEK*
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, ul. Umultowska 87, 61-614 Poznań, Poland email [email protected]
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Abstract

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We show that every continuous self-adjoint functional on the noncommutative Schwartz space can be decomposed into a difference of two positive functionals. Moreover, this decomposition is minimal in the natural sense.

Keywords

Fréchet space(Fréchet) LMC-algebrapositive functionalself-adjoint functionalJordan decomposition

MSC classification

Primary: 46K05: General theory of topological algebras with involution
Secondary: 46H05: General theory of topological algebras 46H35: Topological algebras of operators
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 2 , April 2015 , pp. 322 - 330
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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