Algebras generated by a subnormal operator

Olin, Robert F.; Thomson, James E.

doi:10.1090/S0002-9947-1982-0648094-6

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.

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