Extreme point methods in the study of isometries on certain\n non-commutative spaces

2020/07/02 by Pierre de Jager, de Jager, Pierre, Jurie Conradie +1
Mathematics · #46L52 (Secondary) #47B38 (Primary) #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2007.02324

openalex publication_date 2020/07/02 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper we characterize surjective isometries on certain classes of\nnon-commutative spaces associated with semi-finite von Neumann algebras: the\nLorentz spaces L^w,1, as well as the spaces L¹+L^\∞ and L¹\∩\nL^\∞. The technique used in all three cases relies on characterizations of\nthe extreme points of the unit balls of these spaces. Of particular interest is\nthat the representations of isometries obtained in this paper are global\nrepresentations.\n

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