Linear maps between Banach algebras compressing certain spectral functions

DOI10.1216/rmjm/1181069868zbMath1071.47037OpenAlexW1975292467MaRDI QIDQ1880820

Jian Lian Cui, Jin-Chuan Hou

Publication date: 1 October 2004

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181069868

zbMATH Keywords

Banach algebraslinear preserversJordan homomorphismC*-algebras

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Linear operators on Banach algebras (47B48) Jordan structures on Banach spaces and algebras (17C65) Algebras of operators on Banach spaces and other topological linear spaces (47L10) Transformers, preservers (linear operators on spaces of linear operators) (47B49)

Related Items (26)

Maps preserving the spectrum of generalized Jordan product of operators ⋮ Linear maps preserving the minimum and surjectivity moduli of Hilbert space operators ⋮ Linear maps between operator algebras preserving certain spectral functions ⋮ Minimum and surjectivity moduli preserving in Banach space ⋮ Linear maps preserving regularity in \(C^*\)-algebras ⋮ Maps preserving the \(\partial\)-spectrum of product or triple product of operators ⋮ Additive maps on standard operator algebras preserving parts of the spectrum. ⋮ Linear disjointness preservers of W\(^\ast\)-algebras ⋮ Maps completely preserving spectral functions ⋮ On linear maps preserving certain pseudospectrum and condition spectrum subsets ⋮ Linear maps preserving invertibility or related spectral properties ⋮ Unnamed Item ⋮ Maps preserving peripheral spectrum of generalized Jordan products of self-adjoint operators ⋮ Additive maps between standard operator algebras compressing certain spectral functions ⋮ Approximately spectrum-preserving maps ⋮ Minus partial order and linear preservers ⋮ Maps preserving peripheral spectrum of Jordan semi-triple products of operators ⋮ Characterizing isomorphisms in terms of completely preserving invertibility or spectrum ⋮ Linear maps preserving ideals of C*-algebras ⋮ Inner local spectral radius preservers ⋮ Maps preserving peripheral spectrum of generalized products of operators ⋮ Additive maps onto matrix spaces compressing the spectrum ⋮ Spectral preservers and approximate spectral preservers on operator algebras ⋮ Linear maps preserving Fredholm and Atkinson elements ofC*-algebras ⋮ Surjective linear maps preserving local spectra ⋮ Additive maps on standard operator algebras preserving invertibilities or zero divisors.

Cites Work

• On positive linear maps preserving invertibility
• Spectrum-preserving linear maps
• \(C^*\)-algebras of real rank zero
• A primer on spectral theory
• Spectrum-preserving elementary operators on \(B(X)\)
• Positive elementary operators compressing spectrum
• Invertibility preserving maps preserve idempotents
• Homotopy type of linear groups of two classes of Banach spaces
• Representations, automorphisms, and derivations of some operator algebras
• Linear maps preserving the spectral radius
• Spectrum-Preserving Linear Mappings between Banach Algebras or Jordan-Banach Algebras
• Mappings which Preserve Idempotents, Local Automorphisms, and Local Derivations
• Two characterizations of automorphisms on B(X)
• Local multiplications on algebras spanned by idempotents
• Spectrum preserving linear mappings in Banach algebras
• Point-spectrum-preserving elementary operators on 𝐵(𝐻)
• Linear maps on operator algebras that preserve elements annihilated by a polynomial
• Invertibility preserving linear maps on ℒ(𝒳)
• Rank-preserving linear maps on B(X)
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