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Transactions of the American Mathematical Society

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



Irreducible representations of the $ C\sp{\ast} $-algebra generated by a quasinormal operator

Author: John W. Bunce
Journal: Trans. Amer. Math. Soc. 183 (1973), 487-494
MSC: Primary 47B20; Secondary 46L05
MathSciNet review: 0326461
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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)$.

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Keywords: Irreducible representation, spectrum, quasinormal operator, Hausdorff compactification, regularized transform
Article copyright: © Copyright 1973 American Mathematical Society