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Browder-Type Theorems

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Fredholm and Local Spectral Theory II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2235))

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Abstract

This chapter may be viewed as the part of the book in which the interaction between local spectral theory and Fredholm theory comes into focus. The greater part of the chapter addresses some classes of operators on Banach spaces that have a very special spectral structure. We have seen that the Weyl spectrum σ w(T) is a subset of the Browder spectrum σ b(T) and this inclusion may be proper. In this chapter we investigate the class of operators on complex infinite-dimensional Banach spaces for which the Weyl spectrum and the Browder spectrum coincide. These operators are said to satisfy Browder’s theorem. The operators which satisfy Browder’s theorem have a very special spectral structure, indeed they may be characterized as those operators T ∈ L(X) for which the spectral points λ that do not belong to the Weyl spectrum are all isolated points of the spectrum.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Palermo, Palermo, Italy

    Pietro Aiena

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  1. Pietro Aiena
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Aiena, P. (2018). Browder-Type Theorems. In: Fredholm and Local Spectral Theory II . Lecture Notes in Mathematics, vol 2235. Springer, Cham. https://doi.org/10.1007/978-3-030-02266-2_5

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