TY - JOUR

T1 - Lipschitz continuity of the absolute value and Riesz projections in symmetric operator spaces

AU - Dodds, P. G.

AU - Dodds, T. K.

AU - De Pagter, B.

AU - Sukochev, F. A.

PY - 1997/8/1

Y1 - 1997/8/1

N2 - A principal result of the paper is that ifEis a symmetric Banach function space on the positive half-line with the Fatou property then, for all semifinite von Neumann algebras (M, τ), the absolute value mapping is Lipschitz continuous on the associated symmetric operator spaceE(M, τ) with Lipschitz constant depending only onEif and only ifEhas 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 HaagerupLp-space, provided 1

AB - A principal result of the paper is that ifEis a symmetric Banach function space on the positive half-line with the Fatou property then, for all semifinite von Neumann algebras (M, τ), the absolute value mapping is Lipschitz continuous on the associated symmetric operator spaceE(M, τ) with Lipschitz constant depending only onEif and only ifEhas 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 HaagerupLp-space, provided 1

UR - http://www.scopus.com/inward/record.url?scp=0031206248&partnerID=8YFLogxK

U2 - 10.1006/jfan.1996.3055

DO - 10.1006/jfan.1996.3055

M3 - Article

AN - SCOPUS:0031206248

VL - 148

SP - 28

EP - 69

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 1

ER -