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 | References | Similar Articles | Additional Information

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

Keywords:
Dynamical system,
nonselfadjoint operator algebra,
free action,
Banach module

Article copyright:
© Copyright 1988
American Mathematical Society