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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 property of compact operators


Author: Herbert Kamowitz
Journal: Proc. Amer. Math. Soc. 91 (1984), 231-236
MSC: Primary 47B38; Secondary 46E99
MathSciNet review: 740177
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Abstract: In this note it is shown that if $ T$ is a compact linear operator on a wide class of Banach spaces of the form $ C(S)$, compact $ S$, or $ {L^1}(S,\Sigma ,\mu )$, then $ \left\Vert {I + T} \right\Vert = 1 + \left\Vert T \right\Vert$. This generalizes similar theorems for the spaces $ C\left[ {0,1} \right]$ and $ {L^1}(0,1)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0740177-2
PII: S 0002-9939(1984)0740177-2
Article copyright: © Copyright 1984 American Mathematical Society