Maps onB(H) Preserving Idempotents

DOI10.1080/03081080410001667807zbMath1057.15003OpenAlexW2082534750MaRDI QIDQ4822841

Gregor Dolinar

Publication date: 25 October 2004

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

Full work available at URL: https://doi.org/10.1080/03081080410001667807

zbMATH Keywords

idempotentsHilbert spacenonlinear preserver problem

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Linear transformations, semilinear transformations (15A04)

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Potentials of random walks on trees, Unital and multiplicatively spectrum-preserving surjections between semi-simple commutative Banach algebras are linear and multiplicative, Non-linear preservers of the product of \(C\)-skew symmetry, An algebraic invariant for Jordan automorphisms on \(\beta ( H )\): the set of idempotents, Nonlinear preservers involving quadratic operators, Maps on \({\mathcal B}({\mathcal H})\) preserving involution

Cites Work

• Linear preserver problems: A brief introduction and some special techniques
• On determinant preserver problems
• Maps on matrix algebras preserving idempotents
• Some general techniques on linear preserver problems
• Determinant preserving maps on matrix algebras
• Hua's fundamental theorems of the geometry of matrices and related results
• Automorphisms of the poset of skew projections
• Sums of small numbers of idempotents
• Geometry of symmetric matrices over any field with characteristic other than two
• Mappings which Preserve Idempotents, Local Automorphisms, and Local Derivations
• Maps on Matrix Algebras Preserving Commutativity