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Canonical Operator Space Structures on Non-Commutative Lp Spaces

✍ Scribed by Francesco Fidaleo

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 249 KB
Volume: 169
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1999.3498

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✦ Synopsis

We analyze canonical operator space structures on the non-commutative L p spaces L p ' (M; ., |) constructed by interpolation a la Stein Weiss based on two normal semifinite faithful weights ., | on a W*-algebra M. We show that there is only one canonical (i.e. arising by interpolation) operator space structure on L p (M ) when M and p are kept fixed. Namely, for any n.s.f. weights ., | on M and ' # [0, 1], the spaces L p ' (M; ., |) are all completely isomorphic when they are canonically considered as operator spaces. Finally, we also describe the norms on all matrix spaces M n (L p (M )) which determine such a canonical quantized structure.

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