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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On a question of N. Salinas


Author: Muneo Chō
Journal: Proc. Amer. Math. Soc. 98 (1986), 94-96
MSC: Primary 47B20; Secondary 47A10
DOI: https://doi.org/10.1090/S0002-9939-1986-0848883-8
MathSciNet review: 848883
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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) = \vert\vert{D_T}\vert\vert$? 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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DOI: https://doi.org/10.1090/S0002-9939-1986-0848883-8
Keywords: Joint approximate point spectrum, joint operator norm, doubly commuting $ n$-tuple of hyponormal operators
Article copyright: © Copyright 1986 American Mathematical Society