Irreducible representations of the $C^{\ast }$-algebra generated by a quasinormal operator
HTML articles powered by AMS MathViewer
- by John W. Bunce PDF
- Trans. Amer. Math. Soc. 183 (1973), 487-494 Request permission
Abstract:
For A a quasinormal operator on Hilbert space, we determine the irreducible representations of ${C^ \ast }(A)$, the ${C^ \ast }$-algebra generated by A and the identity. We also explicitly describe the topology on the space of unitary equivalence classes of irreducible representations of ${C^ \ast }(A)$ and calculate the regularized transform of ${C^ \ast }(A)$, thus exhibiting an isomorphic copy of ${C^ \ast }(A)$.References
- Horst Behncke, Structure of certain nonnormal operators, J. Math. Mech. 18 (1968/1969), 103–107. MR 0229082, DOI 10.1512/iumj.1969.18.18010
- Arlen Brown, On a class of operators, Proc. Amer. Math. Soc. 4 (1953), 723–728. MR 59483, DOI 10.1090/S0002-9939-1953-0059483-2
- Arlen Brown, The unitary equivalence of binormal operators, Amer. J. Math. 76 (1954), 414–434. MR 62355, DOI 10.2307/2372582
- John Bunce, Characters on singly generated $C^{\ast }$-algebras, Proc. Amer. Math. Soc. 25 (1970), 297–303. MR 259622, DOI 10.1090/S0002-9939-1970-0259622-4
- John Bunce, The joint spectrum of commuting nonnormal operators, Proc. Amer. Math. Soc. 29 (1971), 499–505. MR 283602, DOI 10.1090/S0002-9939-1971-0283602-7
- John W. Bunce and James A. Deddens, Irreducible representations of the $C^{\ast }$-algebra generated by an $n$-normal operator, Trans. Amer. Math. Soc. 171 (1972), 301–307. MR 306930, DOI 10.1090/S0002-9947-1972-0306930-0
- L. A. Coburn, The $C^{\ast }$-algebra generated by an isometry, Bull. Amer. Math. Soc. 73 (1967), 722–726. MR 213906, DOI 10.1090/S0002-9904-1967-11845-7
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
- J. M. G. Fell, The structure of algebras of operator fields, Acta Math. 106 (1961), 233–280. MR 164248, DOI 10.1007/BF02545788
- J. M. G. Fell, A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space, Proc. Amer. Math. Soc. 13 (1962), 472–476. MR 139135, DOI 10.1090/S0002-9939-1962-0139135-6
- Harry Gonshor, Spectral theory for a class of nonnormal operators. II, Canadian J. Math. 10 (1958), 97–102. MR 92125, DOI 10.4153/CJM-1958-012-5
- A. Gišarde, Tensor products of $C^{\ast }$-algebras, Dokl. Akad. Nauk SSSR 160 (1965), 986–989 (Russian). MR 0176351
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 183 (1973), 487-494
- MSC: Primary 47B20; Secondary 46L05
- DOI: https://doi.org/10.1090/S0002-9947-1973-0326461-2
- MathSciNet review: 0326461