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The ideal structure of certain nonselfadjoint operator algebras


Author: Justin Peters
Journal: Trans. Amer. Math. Soc. 305 (1988), 333-352
MSC: Primary 47D25; Secondary 46H20, 46L55, 46M99
DOI: https://doi.org/10.1090/S0002-9947-1988-0920162-6
MathSciNet review: 920162
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Abstract: Let $ (X,\,\phi )$ be a locally compact dynamical system, and $ {{\mathbf{Z}}^ + }{ \times _\phi }\,{C_0}(X)$ the norm-closed subalgebra of the crossed product $ Z{ \times _\phi }{C_0}(X)$ generated by the nonnegative powers of $ \phi $ in case $ \phi $ is a homeomorphism. If $ \phi $ is just a continuous map, $ {{\mathbf{Z}}^ + }{ \times _\phi }{C_0}$ can still be defined by a crossed product type construction. The ideal structure of these algebras is determined in case $ \phi $ acts freely. A class of strictly transitive Banach modules is described, indicating that for the nonselfadjoint operator algebras considered here, not all irreducible representations are on Hilbert space. Finally in a special case, the family of all invariant maximal right ideals is given.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1988-0920162-6
Keywords: Dynamical system, nonselfadjoint operator algebra, free action, Banach module
Article copyright: © Copyright 1988 American Mathematical Society

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