Automorphisms of the algebra of operators in ${\mathbb L}^p$ preserving conditioning

Volume 120 / 2010

Ryszard Jajte 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 $[0, 1]$.

Authors

  • Ryszard JajteFaculty of Mathematics and Computer Science
    University of /Lódź
    Banacha 22
    90-238 /Lódź, Poland
    e-mail

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