Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T08:22:32.604Z Has data issue: false hasContentIssue false

Nest Representations of TAF Algebras

Published online by Cambridge University Press:  20 November 2018

Alan Hopenwasser
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA email: [email protected]
Justin R. Peters
Affiliation:
Department of Mathematics, Iowa State University, Ames, IA, USA email: [email protected]
Stephen C. Power
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A nest representation of a strongly maximal $\text{TAF}$ algebra $A$ with diagonal $D$ is a representation $\pi $ for which $\text{Lat}\,\pi \left( A \right)$ is totally ordered. We prove that $\ker \,\pi$ is a meet irreducible ideal if the spectrum of $A$ is totally ordered or if (after an appropriate similarity) the von Neumann algebra $\text{ }\!\!\pi\!\!\text{ }{{\left( D \right)}^{\prime \prime }}$ contains an atom.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2000

References

[1] Arveson, W. B. and Josephson, K. B., Operator algebras and measure preserving automorphisms II. J. Funct. Anal. 4(1969), 100134.Google Scholar
[2] Davidson, K. R., Similarity and compact perturbations of nest algebras. J. Reine Angew. Math. 348(1984), 286294.Google Scholar
[3] Donsig, A. P., Hopenwasser, A., Hudson, T. D., Lamoureux, M. P. and Solel, B., Meet irreducible ideals in direct limit algebras. Math. Scand., to appear.Google Scholar
[4] Haagerup, U., Solution of the similarity problem for cyclic representations of C*-algebras. Ann. Math 118(1983), 215240.Google Scholar
[5] Kadison, R. V., On the othogonalization of operator representations. Amer. J. Math. 77(1955), 600620.Google Scholar
[6] Lamoureux, M. P., Nest representations and dynamical systems. J. Funct. Anal. 114(1993), 467492.Google Scholar
[7] Lamoureux, M. P., Ideals in some continuous nonselfadjoint crossed product algebras. J. Funct. Anal. 142(1996), 211248.Google Scholar
[8] Lamoureux, M. P., The topology of ideals in some triangular AF algebras. J. Operator Theory 37(1997), 91109.Google Scholar
[9] Muhly, P. S. and Solel, B., Subalgebras of groupoid C*-algebras. J. Reine Angew. Math. 402(1989), 4175.Google Scholar
[10] Orr, J. L. and Peters, J. R., Some representations of TAF algebras. Pacific J. Math. 167(1995), 129161.Google Scholar
[11] Peters, J. R., Semi-crossed products of C*-algebras. J. Funct. Anal. 59(1984), 498534.Google Scholar
[12] Power, S. C., Classification of analytic crossed product algebras. Bull. London Math. Soc. 24(1992), 368372.Google Scholar
[13] Power, S. C., Limit algebras: An introduction to subalgebras of C*-algebras. Pitman Res. Notes Math. Ser. 278, Longman Scientific and Technical, England, New York, 1992.Google Scholar