0000000000144451

AUTHOR

Muneo Chō

showing 2 related works from this author

Weyl's Theorems and Extensions of Bounded Linear Operators

2012

A bounded operator $T\in L(X)$, $X$ a Banach space, is said to satisfy Weyl's theorem if the set of all spectral points that do not belong to the Weyl spectrum coincides with the set of all isolated points of the spectrum which are eigenvalues and having finite multiplicity. In this article we give sufficient conditions for which Weyl's theorem for an extension $\overline T$ of $T$ (respectively, for $T$) entails that Weyl's theorem holds for $T$ (respectively, for $\overline T$).

Pure mathematicsGeneral MathematicsSpectrum (functional analysis)Extension of bounded operators Weyl type theoremsBanach spaceMultiplicity (mathematics)Extension (predicate logic)Mathematics::Spectral TheoryBounded operatorSet (abstract data type)47A1047A1147A55Settore MAT/05 - Analisi MatematicaBounded function47A53Mathematics::Representation TheoryEigenvalues and eigenvectorsMathematics
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The perturbation classes problem for closed operators

2017

We compare the perturbation classes for closed semi-Fredholm and Fredholm operators with dense domain acting between Banach spaces with the corresponding perturbation classes for bounded semi-Fredholm and Fredholm operators. We show that they coincide in some cases, but they are different in general. We describe several relevant examples and point out some open problems.

Mathematics::Functional AnalysisPure mathematicsMathematics::Operator AlgebrasGeneral Mathematics010102 general mathematicsMathematical analysisBanach spacePerturbation (astronomy)Fredholm integral equationMathematics::Spectral TheoryOperator theory01 natural sciencesFredholm theorysymbols.namesakeMathematics::K-Theory and HomologyBounded function0103 physical sciencessymbols010307 mathematical physics0101 mathematicsMathematicsFilomat
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