TY - JOUR
T1 - Rigid Οℑp structures of non-commutative L p-spaces associated with hyperfinite von Neumann algebras
AU - Junge, Marius
AU - Ruan, Zhong Jin
AU - Xu, Quanhua
PY - 2005
Y1 - 2005
N2 - This paper is devoted to the study of rigid local operator space structures on non-commutative Lp-spaces. We show that for 1 ≤ p ≠ 2 〈, a non-commutative Lp-space Lp(M) is a rigid Οℑp space (equivalently, a rigid Οℑ p space) if and only if it is a matrix orderly rigid Οℑp space (equivalently, a matrix orderly rigid Οℑp, space). We also show that Lp(M) has these local properties if and only if the associated von Neumann algebra M is hyperfinite. Therefore, these local operator space properties on non-commutative Lp-spaces characterize hyperfinite von Neumann algebras.
AB - This paper is devoted to the study of rigid local operator space structures on non-commutative Lp-spaces. We show that for 1 ≤ p ≠ 2 〈, a non-commutative Lp-space Lp(M) is a rigid Οℑp space (equivalently, a rigid Οℑ p space) if and only if it is a matrix orderly rigid Οℑp space (equivalently, a matrix orderly rigid Οℑp, space). We also show that Lp(M) has these local properties if and only if the associated von Neumann algebra M is hyperfinite. Therefore, these local operator space properties on non-commutative Lp-spaces characterize hyperfinite von Neumann algebras.
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U2 - 10.7146/math.scand.a-14945
DO - 10.7146/math.scand.a-14945
M3 - Article
AN - SCOPUS:17744395746
SN - 0025-5521
VL - 96
SP - 63
EP - 95
JO - Mathematica Scandinavica
JF - Mathematica Scandinavica
IS - 1
ER -