Communication on Applied Mathematics and Computation, Volume (28), No (4), Year (2014-12) , Pages (379-389)

#### Title : ( Inequalities for trace on $\tau$-measurable operators )

Citation: BibTeX | EndNote

#### Abstract

Let $\mathfrak{M}$ be a semifinite von Neumann algebra on a Hilbert space equipped with a faithful normal semifinite trace $\tau$. A closed densely defined operator $x$ affiliated with $\mathfrak{M}$ is called $\tau$-measurable if there exists a number $\lambda \geq 0$ such that $\tau \left(e^{|x|}(\lambda,\infty)\right)<\infty$. A number of useful inequalities, which are known for the trace on Hilbert space operators, are extended to trace on $\tau$-measurable operators. In particular, these inequalities imply Clarkson inequalities for $n$-tuples of $\tau$-measurable operators. A general parallelogram law for $\tau$-measurable operators are given as well.

#### Keywords

, Semifinite von Neumann algebra, $\tau$-measurable, operator, trace, Clarkson inequality
برای دانلود از شناسه و رمز عبور پرتال پویا استفاده کنید.

@article{paperid:1045054,
title = {Inequalities for trace on $\tau$-measurable operators},
journal = {Communication on Applied Mathematics and Computation},
year = {2014},
volume = {28},
number = {4},
month = {December},
issn = {1006-6330},
pages = {379--389},
numpages = {10},
keywords = {Semifinite von Neumann algebra; $\tau$-measurable، operator; trace; Clarkson inequality},
}

%T Inequalities for trace on $\tau$-measurable operators