Logarithmic submajorization, uniform majorization and Hölder type inequalities for τ-measurable operators
Logarithmic submajorization, uniform majorization and Hölder type inequalities for τ-measurable operators
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DOI：
10.1016/j.indag.2020.02.004
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发表时间：
2019-10
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影响因子：
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通讯作者：
P. Dodds;T. Dodds;F. Sukochev;D. Zanin
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文献类型：
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作者：
P. Dodds;T. Dodds;F. Sukochev;D. Zanin
我们推广了最初由T. Fack，推广到τ-可测算子的自然代数，它隶属于一个半有限的von Neumann代数，该代数与Haagerup和Schultz在有限情形下定义的代数一致，并且证明了其行列式函数是次乘法的.应用Hölder型不等式通过一般Araki-Lieb-Thirring不等式由于Kosaki和Han和Weyl型定理的一致控制。
We extend the notion of the determinant function Λ, originally introduced by T. Fack for τ-compact operators, to a natural algebra of τ-measurable operators affiliated with a semifinite von Neumann algebra which coincides with that defined by Haagerup and Schultz in the finite case and on which the determinant function is shown to be submultiplicative. Application is given to Hölder type inequalities via general Araki–Lieb–Thirring inequalities due to Kosaki and Han and to a Weyl-type theorem for uniform majorization.