Weyl-Type Theorems

Aiena, Pietro

doi:10.1007/978-3-030-02266-2_6

Cited by 3 publications

(3 citation statements)

References 65 publications

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“…If Q 1 ∈ L(X) and Q 2 ∈ L(Y) are two quasi-nilpotent operators commuting with T and S, respectively. Then, by Corollaries 3.24 and 3.18, of [30], we have that σ(T) = σ(T + Q 1 ),…”

Section: Letmentioning

confidence: 93%

Property (Bv) and Tensor Product

Aponte

Vasanthakumar²,

Jayanthi³

2022

Symmetry

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In this article, a-Browder’s classical theorem is considered through the property (Bv), and we show that if two operators are norm equivalent, then property (Bv) holds for one if and only if it holds for the other. The necessary conditions for the difference of the spectrum and essential approximate point spectrum of the tensor product of two operators coincide with the product of differences between the spectrum and the essential approximate point spectrum of its two factors are investigated. We also discuss the necessary conditions for the tensor product of two operators to verify the property (Bv) and simultaneously give the equivalence between their various spectra with their Browder spectrum, likewise with the Drazin spectrum.

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“…If Q 1 ∈ L(X) and Q 2 ∈ L(Y) are two quasi-nilpotent operators commuting with T and S, respectively. Then, by Corollaries 3.24 and 3.18, of [30], we have that σ(T) = σ(T + Q 1 ),…”

Section: Letmentioning

confidence: 93%

Property (Bv) and Tensor Product

Aponte

Vasanthakumar²,

Jayanthi³

2022

Symmetry

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“…The Fredholm and semi-Fredholm theory on Hilbert and Banach spaces started by studying the integral equations introduced in the pioneering work by Fredholm in 1903 in [6]. After that, the abstract theory of Fredholm and semi-Fredholm operators on Hilbert and Banach spaces was further developed in numerous papers and books such as [1,2]. In addition to classical semi-Fredholm theory on Hilbert and Banach spaces, several generalizations of this theory have been considered.…”

Section: Introductionmentioning

confidence: 99%

On new approach to semi-Fredholm theory in unital C<sup>*</sup>-algebras

Ivkovic

2024

PIGC

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Axiomatic Fredholm theory in unital C*-algebras was established in [D. Kečkić, Z. Lazović, Acta Sci. Math., 83(3-4):629--655, 2017]. Following the pure algebraic approach by Kečkić and Lazović, in the author's paper [S. Ivković, Banach J. Math. Anal., 17:51, 2023] we extended further this theory to axiomatic semi-Fredholm and semi-Weyl theory in unital C*-algebras. However, recently, in [S. Ivković, arXiv:2306.01133] we developed another approach to axiomatic Fredholm theory in unital C*-algebras which is based on the theory of Hilbert modules and is equivalent to the algebraic approach by Kečkić and Lazović. In this paper, we extend further that new Hilbert-module approach from Fredholm theory to semi-Fredholm and semi-Weyl theory in unital C*-algebras. Hence, we provide new proofs to the results in [S. Ivković, Banach J. Math. Anal., 17:51, 2023].

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“…As we have known, Atkinson established a connection between Fredholm operators and the invertible elements in Calkin algebra [2], which indicates that the Fredholm operators can be regarded as "weakened invertible operators". Since then, the research on classical Fredholm theory has received widespread attention and flourishing development, which has promoted the development of spectral theory [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Fredholm Theory Relative to Any Algebra Homomorphisms

Kong,

Wang,

Yang

2024

Mathematics

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In this paper, we give another definition of Ruston elements and almost Ruston elements, which is equivalent to the definitions given by Mouton and Raubenheimer in the case that the homomorphism has a closed range and Riesz property. For two homomorphisms, we consider the preserver problems of Fredholm theory and Fredholm spectrum theory. In addition, we study the spectral mapping theorems of Fredholm (Weyl, Browder, Ruston, and almost Ruston) elements relative to a homomorphism. Last but not least, the dependence of Fredholm theory on three homomorphisms is considered, and meanwhile, the transitivity of Fredholm theory relative to three homomorphisms is illustrated. Furthermore, we consider the Fredholm theory relative to more homomorphisms.

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Weyl-Type Theorems

Cited by 3 publications

References 65 publications

Property (Bv) and Tensor Product

Property (Bv) and Tensor Product

On new approach to semi-Fredholm theory in unital C<sup>*</sup>-algebras

Fredholm Theory Relative to Any Algebra Homomorphisms

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