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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The spectral and Fredholm theory of extensions of bounded linear operators
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by Bruce A. Barnes PDF
Proc. Amer. Math. Soc. 105 (1989), 941-949 Request permission

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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 105 (1989), 941-949
  • MSC: Primary 47A20; Secondary 47A10, 47A53, 47B38
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0955454-4
  • MathSciNet review: 955454