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
SN - 0022-1236
VL - 148
SP - 28
EP - 69
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -