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

Ryszard Jajte

doi:10.4064/cm120-2-6

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

Ryszard Jajte ¹

¹ Faculty of Mathematics and Computer Science University of /Lódź Banacha 22 90-238 /Lódź, Poland

Colloquium Mathematicum, Tome 120 (2010) no. 2, pp. 263-266.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

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 $[0, 1]$.

DOI : 10.4064/cm120-2-6

Keywords: alpha isometric automorphism algebra mathbb bounded linear operators mathbb geq alpha transforms conditional expectations conditional expectations only alpha induced measure preserving isomorphism

Affiliations des auteurs :

Ryszard Jajte ¹

¹ Faculty of Mathematics and Computer Science University of /Lódź Banacha 22 90-238 /Lódź, Poland

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Ryszard Jajte. Automorphisms of the algebra of operators
 in ${\mathbb L}^p$ preserving conditioning. Colloquium Mathematicum, Tome 120 (2010) no. 2, pp. 263-266. doi : 10.4064/cm120-2-6. http://geodesic.mathdoc.fr/articles/10.4064/cm120-2-6/

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