Additive maps preserving nilpotent operators or spectral radius

DOI10.1007/s10114-005-0503-yzbMath1084.47028OpenAlexW2068317641MaRDI QIDQ2581254

Zhaofang Bai, Jin-Chuan Hou

Publication date: 9 January 2006

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

Full work available at URL: https://doi.org/10.1007/s10114-005-0503-y

zbMATH Keywords

spectral radiusnilpotent operatoradditive preserver

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Linear operators on Banach algebras (47B48) Transformers, preservers (linear operators on spaces of linear operators) (47B49)

Related Items (15)

Linear maps preserving C-normal operators ⋮ Maps preserving the truncation of products of operators ⋮ Maps preserving numerical radius or cross norms of products of self-adjoint operators ⋮ Additive maps preserving similarity of operators on Banach spaces ⋮ Non-linear maps preserving singular algebraic operators ⋮ Asymptotic similarity preserving additive maps on \(\mathcal B(X)\) ⋮ Additive maps preserving nilpotent perturbation of scalars ⋮ Additive local spectrum compressors ⋮ Unnamed Item ⋮ Spectral preservers and approximate spectral preservers on operator algebras ⋮ Linear rank one preservers between spaces of matrices with zero trace ⋮ On the idempotency, involution and nilpotency of a linear combination of two matrices ⋮ Similarity preserving linear maps on \(\mathscr{J}\)-subspace lattice algebras ⋮ Additive maps preserving \(r\)-nilpotent perturbation of scalars on \(B(\mathcal{H})\) ⋮ Linear maps and additive maps that preserve operators annihilated by a polynomial

Cites Work

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• Spectrum-preserving linear maps
• Spectrum-preserving additive maps
• Linear preserver problems: A brief introduction and some special techniques
• Linear maps and additive maps that preserve operators annihilated by a polynomial
• Additive mappings preserving operators of rank one
• Linear maps preserving the spectral radius
• Linear Transformations on Algebras of Matrices
• Linear mappings preserving square-zero matrices
• Linear Operators Preserving Similarity Classes and Related Results
• Local multiplications on algebras spanned by idempotents
• Rank-preserving linear maps on B(X)

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