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The spectral and Fredholm theory of extensions of bounded linear operators

Author: Bruce A. Barnes
Journal: Proc. Amer. Math. Soc. 105 (1989), 941-949
MSC: Primary 47A20; Secondary 47A10, 47A53, 47B38
MathSciNet review: 955454
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Abstract: Assume $ T$ is a bounded linear operator on some Banach space $ Y$, and that $ T$ has a bounded extension $ \bar T$ on another space. In general almost nothing can be said concerning the relationship between the spectral and Fredholm properties of $ T$ and $ \bar T$. However, assuming the special condition that the range of $ \bar T$ lies in $ Y$, it is shown that these properties are essentially the same for $ T$ and $ \bar T$.

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Keywords: Extension, spectral theory, Fredholm theory
Article copyright: © Copyright 1989 American Mathematical Society

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