Non-commutative Lorentz spaces associated with a semi-finite von Neumann algebra and applications

Hideki Kosaki

Type: Article

Publication Date: 1981-01-01

Citations: 22

DOI: https://doi.org/10.3792/pjaa.57.303

Abstract

0. Introduction.The purpose of the note is to announce a construction, basic properties, and certain applications of non-com- mutative Lorentz spaces associated with semi-finite von Neumann algebras.At first, non-increasing rearrangements for measurable operators affiliated with a semi-finite yon Neumann algebra are introduced and basic properties are obtained.Then, based on them, non-commutative Lorentz spaces are defined.Since we show that those Lorentz spaces are identified with real interpolation spaces between the semi-finite von Neumann algebra in question and its predual, the abstract Marcinkiewicz theorem is available to our Lorentz spaces.In the last

Locations

Proceedings of the Japan Academy Series A Mathematical Sciences - View - PDF

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