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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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