A generalization of Macaev's theorem to non-commutative \(L^ p\)-spaces
type: Item
instance of: scholarly article
title: A generalization of Macaev's theorem to non-commutative \(L^ p\)-spaces
zbMATH Open document ID: 0618.46052
DOI: 10.1007/BF01199077
author: Earl Berkson
author: Paul S. Muhly
author: T. A. Gillespie
published in: Integral Equations and Operator Theory
publication date: 1987-01-01T00:00:00Z
review text: For \(1<p<\infty\) the non-commutative \(L^ p\)-spaces associated with a von Neumann algebra are shown to belong to the class UMD (that is, to possess the unconditionality property for martingale differences). With the aid of a recent result of the authors, which permits the classical Hilbert transform to be transferred to UMD spaces, a generalization of Macaev's theorem to non-commutative \(L^ p\)-spaces is introduced. This generalization utilizes the Hilbert kernel in a central role, broadens the ''harmonic conjugation'' aspects of Macaev's theorem, and provides a universal bound depending only on p.
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 46L30
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 60G46
zbMATH DE Number: 4002832
zbMATH Keywords: non-commutative \(L^ p\)-spaces associated with a von Neumann algebra
zbMATH Keywords: class UMD
zbMATH Keywords: unconditionality property for martingale differences
zbMATH Keywords: Hilbert transform
zbMATH Keywords: generalization of Macaev's theorem to non-commutative \(L^ p\)-spaces
zbMATH Keywords: Hilbert kernel
zbMATH Keywords: harmonic conjugation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4002832