## The ideal structure of certain nonselfadjoint operator algebras

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- by Justin Peters PDF
- Trans. Amer. Math. Soc.
**305**(1988), 333-352 Request permission

## 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.## References

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## Additional Information

- © Copyright 1988 American Mathematical Society
- 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