摘要: Let
be a semifinite von Neumann algebra. We equip the associated noncommutative 
-spaces with their natural operator space structure introduced by Pisier via complex interpolation. On the other hand, for 



let

























be equipped with the operator space structure via real interpolation as defined by the second named author (J. Funct. Anal. 139 (1996), 500——539). We show that













completely isomorphically if and only if

is finite dimensional. This solves in the negative the three problems left open in the quoted work of the second author. \\ We also show that for





and





with


































with equivalent norms, i.e., at the Banach space level if and only if

is isomorphic, as a Banach space, to a commutative von Neumann algebra. \\ Our third result concerns the following inequality:





































for any finite sequence











, where







and





. If

is not isomorphic, as a Banach space, to a commutative von Meumann algebra, then this inequality holds if and only if



.
中图分类号:
Marius JUNGE, Quanhua XU. NOTES ON REAL INTERPOLATION OF OPERATOR Lp-SPACES[J]. 数学物理学报(英文版), 2021, 41(6): 2173-2182.
Marius JUNGE, Quanhua XU. NOTES ON REAL INTERPOLATION OF OPERATOR Lp-SPACES[J]. Acta mathematica scientia,Series B, 2021, 41(6): 2173-2182.