Algebras generated by a subnormal operator
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- by Robert F. Olin and James E. Thomson PDF
- Trans. Amer. Math. Soc. 271 (1982), 299-311 Request permission
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.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- 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