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NOTES ON REAL INTERPOLATION OF OPERATOR L_(p)-SPACES
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作者 marius junge Quanhua XU 《Acta Mathematica Scientia》 SCIE CSCD 2021年第6期2173-2182,共10页
Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(... Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(L_(∞)(M),L_(1)(M)_(1/p,p)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 Lp,p(M)=Lp(M)completely isomorphically if and only if M 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 1<p<∞and 1≤q≤∞with p 6=q,(L_(∞)(M;l_(q)),L_(1)(M;l_(q)_(1/p,p)=L_(p)(M;l_(q)with equivalent norms,i.e.,at the Banach space level if and only if M is isomorphic,as a Banach space,to a commutative von Neumann algebra.Our third result concerns the following inequality:||(∑iixtq)^(1/q)||lp(M)≤||(∑iixit)^(1/q)||lp(M),for any finite sequence(xi)⊂L+p(M),where 0<r<q<∞and 0<p≤∞.If M is not isomorphic,as a Banach space,to a commutative von Meumann algebra,then this inequality holds if and only if p≥r. 展开更多
关键词 operator spaces L_(p)-spaces real interpolation column Hilbertian spaces
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量子信道的熵不确定性原理和强次可加性
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作者 高力 marius junge Nicholas LaRacuente 《中国科学:数学》 CSCD 北大核心 2023年第12期1631-1652,共22页
本文得到了两个量子信道的熵不确定性关系,推广了Frank和Lieb关于量子测量的工作.本文的证明基于量子熵的强次可加性的推广.本文也推广了Petz相对熵的强次可加性.
关键词 量子信道 不确定性原理 强次可加性 非交换Lp空间
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