Local Spectral Properties Under Conjugations

Aiena, Pietro; Burderi, Fabio; Triolo, Salvatore

doi:10.1007/s00009-021-01731-7

Cited by 4 publications

(2 citation statements)

References 22 publications

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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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Section: Introductionmentioning

confidence: 99%

Fredholm Theory Relative to Any Algebra Homomorphisms

Kong,

Wang,

Yang

2024

Mathematics

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“…Recall from [16] that a conjugation on K is a map C : K −→ K which is antilinear, involutive (C 2 = I. Moreover, C satisfies the following properties: See [5,12] for properties of conjugation operators.…”

Section: Introductionmentioning

confidence: 99%

On k-Quasi-(m, n, C)-Isosymmetric Operators

Gherairi,

Maqbul Saqer Alruwaili,

Ould Ahmedmahmoud

2024

Hacettepe Journal of Mathematics and Statistics

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We study the set of k-quasi-(m, n,C)-isosymmetric operators. This family extends the set of (m, , n,C)-isosymmetric operators. In the present article, we give operator matrix representation of k-quasi-(m, , n,C)-isosymmetric operator in order to obtain some structural properties for such operators. we show that if R is k-quasi-(m, n,C)-isosymmetric, then Rq is a k-quasi-(m, n,C)-isosymmetric operator. We show that the product of an k1-quasi-(m1, n1,C)-isosymmetric and an n2-quasi-(m2, n2,C)-isosymmetric which are Cdouble commuting is an max{k1, k2}-quasi-(m1 + m2 − 1, n1 + n2 − 1,C)-isosymmetry under suitable conditions. In particular, we prove the stability of perturbation of kquasi-( m, n,C)-isosymmetric operator by a nilpotent operator of order p under suitable conditions. Moreover, we give some results about the joint approximate spectrum of a k-quasi-(m, n,C)-isosymmetric operators.

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