Some results on higher order isometries and symmetries: products and sums with a nilpotent operator

DOI10.1016/j.laa.2014.09.044zbMath1326.47013OpenAlexW1978900862MaRDI QIDQ486229

Mark Stankus, Caixing Gu

Publication date: 14 January 2015

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2014.09.044

zbMATH Keywords

Hilbert spacetensor productslinear transformationselementary operators\(m\)-isometric operator\(n\)-symmetric operatornilpotent operators

Mathematics Subject Classification ID

Equations involving linear operators, with operator unknowns (47A62) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Special classes of linear operators (47B99)

Related Items (22)

Arithmetic progressions and its applications to \((m,q)\)-isometries: a survey ⋮ Unnamed Item ⋮ Elementary properties of isometries on a Hilbert space ⋮ On higher order selfadjoint operators ⋮ \((A,m)\)-isometries on Hilbert spaces ⋮ Linear preservers of \(m\)-selfadjoint operators and high-order isometries ⋮ Exponentially \(m\)-isometric operators on Hilbert spaces ⋮ On [m,C-symmetric Operators] ⋮ Isometric, symmetric and isosymmetric commuting \(d\)-tuples of Banach space operators ⋮ The 3-isometric lifting theorem ⋮ Elementary operators which are \(m\)-isometries ⋮ Multivariable Bergman shifts and Wold decompositions ⋮ The n-inverses of a matrix ⋮ Some results on higher orders quasi-isometries ⋮ Unnamed Item ⋮ Decomposing algebraic \(m\)-isometric tuples ⋮ Algebraic properties of operator roots of polynomials ⋮ \(m\)-isometric operators and their local properties ⋮ Some examples of \(m\)-isometries ⋮ Functional calculus for m-isometries and related operators on Hilbert spaces and Banach spaces ⋮ Structures of left n-invertible operators and their applications ⋮ The \((m,q)\)-isometric weighted shifts on \(l_{p}\) spaces

Cites Work

• Tensor product of \(n\)-isometries
• Isometric properties of elementary operators
• Nonnormal dilations, disconjugacy and constrained spectral factorization
• Classification of hereditary matrices
• \(m\)-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
• Hereditary Classes of Operators and Matrices
• Infinite Dimensional Jordan Operators and Sturm-Liouville Conjugate Point Theory
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Some results on higher order isometries and symmetries: products and sums with a nilpotent operator