Operators with 𝐶*-algebra generated by a unilateral shift

Conway, John B.; McGuire, Paul

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

Operators with $C^{\ast }$-algebra generated by a unilateral shift
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by John B. Conway and Paul McGuire

Trans. Amer. Math. Soc. 284 (1984), 153-161

DOI: https://doi.org/10.1090/S0002-9947-1984-0742417-7

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Abstract:

If $T$ is an operator on a Hilbert space $\mathcal {H}$, this paper gives necessary and sufficient conditions on $T$ such that ${C^{\ast } }(T)$, the ${C^{\ast } }$-algebra generated by $T$, is generated by a unilateral shift of some multiplicity. This result is then specialized to the cases in which $T$ 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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