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On Young-type inequalities of measurable operators
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2021-04-27 , DOI: 10.1080/03081087.2021.1920877
Turdebek N. Bekjan 1 , Myrzagali N. Ospanov 2
Affiliation  

Let (M,τ) be a semi-finite von Neumann algebra, L0(M) be the set of all τ-measurable operators and μt(x) be the generalized singular number of xL0(M). We proved that if 1<p,q<,1p+1q=1, r2min{1p,1q} and x,yL0(M), then the Young-type inequality μt(|xy|r)μt(1p|x|pr+1q|y|qr), for all t>0 holds.



中文翻译:

关于可测算符的杨型不等式

(,τ)是一个半有限冯诺依曼代数,大号0()是所有τ可测算子的集合,并且μ(X)是广义单数X大号0(). 我们证明了如果1个<p,q<,1个p+1个q=1个,r2个分钟{1个p,1个q}X,大号0(), 那么杨型不等式μ(|X|r)μ(1个p|X|pr+1个q||qr),对于所有t >0 成立。

更新日期:2021-04-27
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