Displaying similar documents to “A characterization of some subsets of S-essential spectra of a multivalued linear operator”

B-Fredholm and Drazin invertible operators through localized SVEP

M. Amouch, H. Zguitti (2011)

Mathematica Bohemica

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Let X be a Banach space and T be a bounded linear operator on X . We denote by S ( T ) the set of all complex λ ∈ ℂ such that T does not have the single-valued extension property at λ . In this note we prove equality up to S ( T ) between the left Drazin spectrum, the upper semi-B-Fredholm spectrum and the semi-essential approximate point spectrum. As applications, we investigate generalized Weyl’s theorem for operator matrices and multiplier operators.

Spectra originating from semi-B-Fredholm theory and commuting perturbations

Qingping Zeng, Qiaofen Jiang, Huaijie Zhong (2013)

Studia Mathematica

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Burgos, Kaidi, Mbekhta and Oudghiri [J. Operator Theory 56 (2006)] provided an affirmative answer to a question of Kaashoek and Lay and proved that an operator F is of power finite rank if and only if σ d s c ( T + F ) = σ d s c ( T ) for every operator T commuting with F. Later, several authors extended this result to the essential descent spectrum, left Drazin spectrum and left essential Drazin spectrum. In this paper, using the theory of operators with eventual topological uniform descent and the technique used...

Semi-Browder operators and perturbations

Vladimir Rakočević (1997)

Studia Mathematica

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An operator in a Banach space is called upper (resp. lower) semi-Browder if it is upper (lower) semi-Fredholm and has a finite ascent (resp. descent). An operator in a Banach space is called semi-Browder if it is upper semi-Browder or lower semi-Browder. We prove the stability of the semi-Browder operators under commuting Riesz operator perturbations. As a corollary we get some results of Grabiner [6], Kaashoek and Lay [8], Lay [11], Rakočević [15] and Schechter [16].

The index for Fredholm elements in a Banach algebra via a trace II

Jacobus J. Grobler, Heinrich Raubenheimer, Andre Swartz (2016)

Czechoslovak Mathematical Journal

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We show that the index defined via a trace for Fredholm elements in a Banach algebra has the property that an index zero Fredholm element can be decomposed as the sum of an invertible element and an element in the socle. We identify the set of index zero Fredholm elements as an upper semiregularity with the Jacobson property. The Weyl spectrum is then characterized in terms of the index.

Characterisations of open multivalued linear operators

T. Álvarez (2006)

Studia Mathematica

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The class of all open linear relations is characterised in terms of the restrictions of the linear relations to finite-codimensional subspaces. As an application, we establish two results, the first of which shows that an upper semi-Fredholm linear relation retains its index under finite rank perturbations, and the second is a density theorem for lower bounded linear relations that have closed range. Results of Labuschagne and of Mbekhta about linear operators are covered.

The index for Fredholm elements in a Banach algebra via a trace

J. J. Grobler, H. Raubenheimer (2008)

Studia Mathematica

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We show that the existence of a trace on an ideal in a Banach algebra provides an elegant way to develop the abstract index theory of Fredholm elements in the algebra. We prove some results on the problem of the equality of the nonzero exponential spectra of elements ab and ba and use the index theory to formulate a condition guaranteeing this equality in a quotient algebra.