On the structure of Banach algebras associated with automorphisms
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A. V. Lebedev
Translated by: O. Khleborodova - Trans. Moscow Math. Soc. 2005, 105-142
- DOI: https://doi.org/10.1090/S0077-1554-05-00153-6
- Published electronically: November 18, 2005
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Abstract:
We study the structure of the Banach algebra $B(A, T_g )$ generated by a Banach algebra $A$ of operators in a Banach space $D$ and a group $\{ T_g \}_{g \in G}$ of isometries of $D$ such that $T_g A T^{-1}_g = A$. We analyze relations between the existence of an expectation from $B(A, T_g )$ to $A$, topological (metric) freeness of the action by automorphisms of the algebra $A$ induced by $T_g$, and the dual action of the group $G$ on $B(A, T_g )$. The obtained results are applied to the description of the structure of Banach algebras generated by “weighted composition operators” in various spaces.References
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Bibliographic Information
- A. V. Lebedev
- Affiliation: Belarus State University, Minsk 220050, Belarus
- Address at time of publication: Institute of Mathematics, University of Białystok, Akademicka 2, Białystok 15-267, Poland
- MR Author ID: 194196
- Email: lebedev@bsu.by
- Published electronically: November 18, 2005
- © Copyright 2005 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2005, 105-142
- MSC (2000): Primary 46L05
- DOI: https://doi.org/10.1090/S0077-1554-05-00153-6
- MathSciNet review: 2193431