A survey on preservers of spectra and local spectra

DOI10.1090/conm/638/12810zbMath1353.47070OpenAlexW4235922633MaRDI QIDQ2827660

Abdellatif Bourhim, Javad Mashreghi

Publication date: 20 October 2016

Published in: Invariant Subspaces of the Shift Operator (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/638/12810

zbMATH Keywords

operatorsspectral radiusmatricesBanach algebrasFredholm theorylocal spectral radiusgeneralized invertibilityinner local spectral radiusKaplansky's conjecturespectral isometrieslinear and nonlinear preserversminimum and reduced minimum moduli

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Spectrum, resolvent (47A10) Perturbation theory of linear operators (47A55) (Semi-) Fredholm operators; index theories (47A53) Linear operators on Banach algebras (47B48) Research exposition (monographs, survey articles) pertaining to operator theory (47-02) Structure theory of linear operators (47A65) Spectral sets of linear operators (47A25) Transformers, preservers (linear operators on spaces of linear operators) (47B49)

Related Items (48)

A note on local spectral subspace preservers ⋮ Maps preserving some spectral domains of skew products of operators ⋮ Maps preserving the local spectrum of some matrix products ⋮ Maps compressing and expanding the numerical range onC^*-algebras ⋮ Lie product and local spectrum preservers ⋮ Jordan product and local spectrum preservers ⋮ On maps preserving operators of local spectral radius zero ⋮ Maps preserving local spectral subspaces of generalised product of operators ⋮ Nonlinear maps preserving certain subspaces of Lie product of operators ⋮ Maps preserving matrices of local reduced minimum modulus zero at a fixed vector ⋮ Maps preserving the local reduced minimum modulus ⋮ Unnamed Item ⋮ Nonsurjective numerical radius isometries between matrix algebras ⋮ Automatic continuity for linear surjective maps compressing the local spectrum at fixed vectors ⋮ Preservers of the local spectral radii ⋮ Nonlinear maps preserving the reduced minimum modulus of operators ⋮ Maps preserving the local spectral subspace of product or Jordan triple product of operators ⋮ Condition spectrum of rank one operators and preservers of the condition spectrum of skew product of operators ⋮ Linear Surjective Maps Preserving at Least One Element from the Local Spectrum ⋮ Unnamed Item ⋮ Linear maps preserving operators of inner local spectral radius zero at some fixed vector ⋮ Additive maps preserving matrices of inner local spectral radius zero at some fixed vector ⋮ Spectrum and local spectrum preservers of skew Lie products of matrices ⋮ Multiplicatively pseudo spectrum-preserving maps ⋮ Recent progress on local spectrum-preserving maps ⋮ Maps preserving the local spectrum of Jordan product of matrices ⋮ Unnamed Item ⋮ Multiplicatively local spectrum-preserving maps ⋮ Non-surjective spectral isometries on matrix spaces ⋮ Non-linear modular Birkhoff-James orthogonality preservers between spaces of continuous functions ⋮ On maps compressing the numerical range between \(C^*\)-algebras ⋮ Unnamed Item ⋮ Inner local spectral radius preservers ⋮ Continuous maps preserving local spectra of matrices ⋮ Maps preserving the peripheral local spectrum of some product of operators ⋮ Nonlinear maps preserving the local spectral subspace ⋮ Nonlinear commutant preservers ⋮ Nonlinear maps preserving the inner local spectral radius ⋮ Nonlinear maps preserving the minimum and surjectivity moduli ⋮ Maps preserving the local spectrum of skew-product of operators ⋮ Linear Maps Preserving Matrices of Local Spectral Radius Zero at a Fixed Vector ⋮ Local spectral subspace preservers ⋮ Maps preserving the inner local spectral radius zero of generalized product of operators ⋮ On the local spectral properties of the left multiplication operators ⋮ Maps preserving the pseudo spectrum of skew triple product of operators ⋮ Maps preserving the local spectral radius zero of generalized product of operators ⋮ Maps preserving the spectrum of polynomial products of matrices ⋮ Maps that preserve the local spectral subspace of generalized product of operators

This page was built for publication: A survey on preservers of spectra and local spectra