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Transactions of the American Mathematical Society

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

 

 

Algebras generated by a subnormal operator


Authors: Robert F. Olin and James E. Thomson
Journal: Trans. Amer. Math. Soc. 271 (1982), 299-311
MSC: Primary 47D25; Secondary 47B20
DOI: https://doi.org/10.1090/S0002-9947-1982-0648094-6
MathSciNet review: 648094
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Abstract: We use the notion of generalized Toeplitz operators to obtain some basic results concerning the $ {C^{\ast}}$-algebra generated by a subnormal operator. We apply these results to problems concerning the intersection of $ {C^{\ast}}(S)$ with rationally closed algebras generated by $ S$. In particular, we prove that $ {C^{\ast}}(S) \cap \mathcal{W}(S) = \{ f(S):f \in R({\sigma _{\mathcal{W}(S)}}(S))\} $. The spectral inclusion property for generalized Toeplitz operators with symbols in $ {P^\infty }(\mu ) + C(\sigma (N))$ is also considered.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0648094-6
Article copyright: © Copyright 1982 American Mathematical Society