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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A simple example of a normal operator $ T$ on a Banach space such that $ r(T)<\Vert T\Vert $


Authors: Muneo Chō and Hiroyasu Yamaguchi
Journal: Proc. Amer. Math. Soc. 108 (1990), 143
MSC: Primary 47B15; Secondary 15A60, 47A10
MathSciNet review: 990417
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Abstract: Bonsall and Duncan's book ([1, Theorem 25.6]) exhibits a normal element $ h + ik$ of a Banach algebra such that $ r(h + ik) < \vert\vert h + ik\vert\vert$. In this paper, we will give a simpler example of a normal operator $ T$ on a Banach space such that $ r(T) < \vert\vert T\vert\vert$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0990417-2
PII: S 0002-9939(1990)0990417-2
Keywords: Banach space, normal operator, operator norm, spectral radius
Article copyright: © Copyright 1990 American Mathematical Society