Automorphisms of the algebra of operators in ${\mathbb L}^p$ preserving conditioning
Volume 120 / 2010
Colloquium Mathematicum 120 (2010), 263-266
MSC: 47D30, 46E30, 28D05.
DOI: 10.4064/cm120-2-6
Abstract
Let $\alpha$ be an isometric automorphism of the algebra ${\mathbb B}_p$ of bounded linear operators in ${\mathbb L}^p[0, 1]$ $(p\geq 1)$. Then $\alpha$ transforms conditional expectations into conditional expectations if and only if $\alpha$ is induced by a measure preserving isomorphism of $[0, 1]$.
