Common properties of the operator products in local spectral theory

DOI10.1007/s10114-015-5116-5zbMath1327.47004OpenAlexW2397011395MaRDI QIDQ889443

Kai Yan, Xiao Chun Fang

Publication date: 6 November 2015

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-015-5116-5

zbMATH Keywords

common propertyJacobson's lemmalocal spectral theoryoperator equation set

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Perturbation theory of linear operators (47A55) (Semi-) Fredholm operators; index theories (47A53) Local spectral properties of linear operators (47A11)

Related Items (18)

Extensions of Jacobson's lemma for Drazin inverses ⋮ On Hirano inverses in rings ⋮ Cline’s formula for g-Drazin inverses in a ring ⋮ The generalized inverses of the products of two elements in a ring ⋮ Generalized Hirano inverses in rings ⋮ Recent progress on local spectrum-preserving maps ⋮ Weak inverses of products — Cline’s formula meets Jacobson lemma ⋮ Generalized Jacobson’s Lemma in a Banach algebra ⋮ New extensions of Jacobson's lemma and Cline's formula ⋮ New extensions of Cline’s formula for generalized inverses ⋮ Generalized Jacobson's lemma for Drazin inverses and its applications ⋮ The generalized and pseudo n-strong Drazin inverses in rings ⋮ Extended \(g\)-Drazin inverse in a Banach algebra ⋮ On Drazin spectral equation for the operator products ⋮ On Jacobson's lemma and Cline's formula for Drazin inverses ⋮ Generalized Cline’s formula and common spectral property ⋮ Back to the common spectral properties of operators satisfying AkBkAk = Ak+1 and BkAkBk = Bk+1 ⋮ Extension of generalized strong Drazin inverse

Cites Work

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• On the Dunford property \((C)\) for bounded linear operators \(RS\) and \(SR\)
• Common properties of operators \(RS\) and \(SR\) and \(p\)-hyponormal operators
• w-hyponormal operators are subscalar
• Common properties of bounded linear operators \(AC\) and \(BA\): local spectral theory
• Local spectral theory of linear operators RS and SR
• Common operator properties of the linear operators 𝑅𝑆 and 𝑆𝑅
• Extensions of Jacobson's Lemma
• Spectral Mapping Theorems
• Spectral theory of linear operators and spectral systems in Banach algebras

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