Operators with 𝐶*-algebra generated by a unilateral shift

Conway, John B.; McGuire, Paul

doi:10.1090/S0002-9947-1984-0742417-7

Operators with $C\sp{\ast}$ -algebra generated by a unilateral shift

Authors: John B. Conway and Paul McGuire
Journal: Trans. Amer. Math. Soc. 284 (1984), 153-161
MSC: Primary 47B20; Secondary 47C15
DOI: https://doi.org/10.1090/S0002-9947-1984-0742417-7
MathSciNet review: 742417
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Abstract: If is an operator on a Hilbert space $\mathcal{H}$ , this paper gives necessary and sufficient conditions on such that ${C^{\ast} }(T)$ , the ${C^{\ast} }$ -algebra generated by , is generated by a unilateral shift of some multiplicity. This result is then specialized to the cases in which is a hyponormal or subnormal operator. In particular, it is shown how to prove a recent conjecture of C. R. Putnam as a consequence of our result.

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