Algebraic properties of operator roots of polynomials

DOI10.1016/j.jmaa.2014.07.074zbMath1297.47013OpenAlexW2018508183MaRDI QIDQ743191

Trieu Le

Publication date: 23 September 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.07.074

zbMATH Keywords

nilpotent operator\(m\)-isometry\(m\)-selfadjoint operatorhereditary roots

Mathematics Subject Classification ID

Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Functional calculus for linear operators (47A60) Perturbation theory of linear operators (47A55)

Related Items (14)

Arithmetic progressions and its applications to \((m,q)\)-isometries: a survey ⋮ Elementary properties of isometries on a Hilbert space ⋮ Expansive operators which are power bounded or algebraic ⋮ On higher order selfadjoint operators ⋮ Left m-invertibility by the adjoint of Drazin inverse and m-selfadjointness of Hilbert spaces ⋮ \((A,m)\)-isometries on Hilbert spaces ⋮ Isometric, symmetric and isosymmetric commuting \(d\)-tuples of Banach space operators ⋮ Structure of \(n\)-quasi left \(m\)-invertible and related classes of operators ⋮ On \((m, P)\)-expansive operators: products, perturbation by nilpotents, Drazin invertibility ⋮ Structure of elementary operators defining \(m\)-left invertible, \(m\)-selfadjoint and related classes of operators ⋮ Unnamed Item ⋮ Decomposing algebraic \(m\)-isometric tuples ⋮ \(m\)-isometric operators and their local properties ⋮ Some examples of \(m\)-isometries

Cites Work

• Unnamed Item
• Tensor product of \(n\)-isometries
• Some results on higher order isometries and symmetries: products and sums with a nilpotent operator
• \(m\)-isometric commuting tuples of operators on a Hilbert space
• Classification of hereditary matrices
• Perturbation of \(m\)-isometries by nilpotent operators
• \(m\)-isometric transformations of Hilbert space. I
• \(m\)-isometric transformations of Hilbert space. II
• \(m\)-isometric transformations of Hilbert space. III
• Products of \(m\)-isometries
• \(m\)-isometries, \(n\)-symmetries and other linear transformations which are hereditary roots
• An isometry plus a nilpotent operator is an \(m\)-isometry. Applications
• Elementary operators which are \(m\)-isometries
• Hereditary Classes of Operators and Matrices
• Infinite Dimensional Jordan Operators and Sturm-Liouville Conjugate Point Theory

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