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Lipschitz Continuity of the Absolute Value and Riesz Projections in Symmetric Operator Spaces

✍ Scribed by P.G Dodds; T.K Dodds; B de Pagter; F.A Sukochev

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
531 KB
Volume
148
Category
Article
ISSN
0022-1236

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✦ Synopsis

A principal result of the paper is that if E is a symmetric Banach function space on the positive half-line with the Fatou property then, for all semifinite von Neumann algebras (M, {), the absolute value mapping is Lipschitz continuous on the associated symmetric operator space E(M, {) with Lipschitz constant depending only on E if and only if E has non-trivial Boyd indices. It follows that if M is any von Neumann algebra, then the absolute value map is Lipschitz continuous on the corresponding Haagerup L p -space, provided 1<p< .

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