Injective Envelopes of Separable C*-algebras
Characterisations of those separable C*-algebras that have type I injective envelopes or W*-algebra injective envelopes are presented.
math.OA↗
arXiv subjects
Douglas R. Farenick
Publications and source records attributed to Douglas R. Farenick.
Young's Inequality in Semifinite von Neumann Algebras
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 $\t(\cdot)$ 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 $a,b\in M$, $\t(|ab|)\le p^{-1}\t(a^p)+ q^{-1}\t(b^q)$, with equality holding (in the cases where $p^{-1}\t(a^p)+ q^{-1}\t(b^q)<\infty$) if and only if $b^q=a^p$.
math.OA↗