6533b827fe1ef96bd1286e61

RESEARCH PRODUCT

Browder-Type Theorems

Pietro Aiena

subject

Mathematics::Functional AnalysisPure mathematicssymbols.namesakeClass (set theory)Spectral theorySpectrum (functional analysis)Spectral structuresymbolsBanach spaceType (model theory)Fredholm theoryMathematics

description

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 σw(T) is a subset of the Browder spectrum σb(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.

yearjournalcountryeditionlanguage
2018-01-01
https://doi.org/10.1007/978-3-030-02266-2_5