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Transactions of the Moscow Mathematical Society

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On the structure of Banach algebras associated with automorphisms


Author: A. V. Lebedev
Translated by: O. Khleborodova
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 66 (2005).
Journal: Trans. Moscow Math. Soc. 2005, 105-142
MSC (2000): Primary 46L05
DOI: https://doi.org/10.1090/S0077-1554-05-00153-6
Published electronically: November 18, 2005
MathSciNet review: 2193431
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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.


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Additional 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
Email: lebedev@bsu.by

DOI: https://doi.org/10.1090/S0077-1554-05-00153-6
Published electronically: November 18, 2005
Article copyright: © Copyright 2005 American Mathematical Society

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