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Young's Inequality in Semifinite von Neumann Algebras | Douglas R. Farenick
; S. Mahmoud Manjegani
; | Date: |
25 Mar 2003 | Subject: | Operator Algebras MSC-class: 46L05 (Primary), 47A60 (Secondary) | math.OA | Abstract: | This paper formulates Young-type inequalities for singular values (or $s$-numbers) and traces in the context of von Neumann algebras. In particular, it shown that if $ (cdot)$ is a faithful semifinite normal trace on a semifinite von Neumann algebra $M$ and if $p$ and $q$ are positive real numbers for which $p^{-1}+q^{-1}=1$, then, for all positive operators $a,bin M$, $ (|ab|)le p^{-1} (a^p)+ q^{-1} (b^q)$, with equality holding (in the cases where $p^{-1} (a^p)+ q^{-1} (b^q) | Source: | arXiv, math.OA/0303318 | Services: | Forum | Review | PDF | Favorites |
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