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

Published online by Cambridge University Press:  06 August 2021

PIERRE DE JAGER
Affiliation:
Department of Mathematical Sciences, University of South Africa, P.O. Box, 392, Pretoria 0003, South Africa e-mail: dejagp@unisa.ac.za
JURIE CONRADIE
Affiliation:
Department of Mathematics and Applied Mathematics, University of Cape Town, Cape Town, South Africa e-mail: jurie.conradie@uct.ac.za

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.

Type
Research Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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