On a question of N. Salinas

Chō, Muneo

doi:10.1090/S0002-9939-1986-0848883-8

On a question of N. Salinas
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by Muneo Chō

Proc. Amer. Math. Soc. 98 (1986), 94-96

DOI: https://doi.org/10.1090/S0002-9939-1986-0848883-8

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Abstract:

In [5], Salinas asked the following question: If $T = ({T_1}, \ldots ,{T_n})$ consists of commuting hyponormal operators, is it true that (1) $\delta (T - \lambda ) = d(\lambda ,{\sigma _\pi }(T))$ and (2) ${r_\pi }(T) = ||{D_T}||$? He proved that, for a doubly commuting $n$-tuple of quasinormal operators, (2) was true and (1) was true for $\lambda = 0$. In this paper we shall show that (2) holds for a doubly commuting $n$-tuple of hyponormal operators and give an example of a subnormal operator which does not satisfy (1).

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