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EXTREME POINT METHODS IN THE STUDY OF ISOMETRIES ON CERTAIN NONCOMMUTATIVE SPACES

Part of: Selfadjoint operator algebras Special classes of linear operators

Published online by Cambridge University Press:  06 August 2021

PIERRE DE JAGER  and
JURIE CONRADIE
PIERRE DE JAGER
Affiliation:
Department of Mathematical Sciences, University of South Africa, P.O. Box, 392, Pretoria 0003, South Africa e-mail: [email protected]
JURIE CONRADIE
Affiliation:
Department of Mathematics and Applied Mathematics, University of Cape Town, Cape Town, South Africa e-mail: [email protected]
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Abstract

In this paper, we characterize surjective isometries on certain classes of noncommutative spaces associated with semi-finite von Neumann algebras: the Lorentz spaces $L^{w,1}$ , as well as the spaces $L^1+L^\infty$ and $L^1\cap L^\infty$ . The technique used in all three cases relies on characterizations of the extreme points of the unit balls of these spaces. Of particular interest is that the representations of isometries obtained in this paper are global representations.

MSC classification

Primary: 47B38: Operators on function spaces (general)
Secondary: 46L52: Noncommutative function spaces
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 2 , May 2022 , pp. 462 - 483
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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