Linear maps that preserve the commutant, double commutant or the lattice of invariant subspaces

DOI10.1080/03081089508818345zbMath0817.47006OpenAlexW2041117866MaRDI QIDQ4322532

Ahmed Ramzi Sourour, Ali-Akbar Jafarian

Publication date: 9 February 1995

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

Full work available at URL: https://doi.org/10.1080/03081089508818345

zbMATH Keywords

reducing subspaceslattice of invariant subspacesdouble commutant

Mathematics Subject Classification ID

Invariant subspaces of linear operators (47A15) Commutators, derivations, elementary operators, etc. (47B47)

Related Items (17)

Maps preserving some spectral domains of skew products of operators ⋮ On the some spectral domains in the spectrum preserves ⋮ Biseparating maps between operator algebras. ⋮ Jordan product and fixed points preservers ⋮ Lie centralizers and commutant preserving maps on generalized matrix algebras ⋮ General preservers of invariant subspace lattices ⋮ Invertible Preservers and Algebraic Groups II: Preservers of Similarity Invariants and Overgroups ofPSL_n(F) ⋮ Nonlinear fixed points preservers ⋮ Nonlinear maps preserving solvability ⋮ Nonlinear maps preserving the local spectral subspace ⋮ Nonlinear commutant preservers ⋮ Nonlinear commuting maps on ℒ (X) ⋮ Local spectral subspace preservers ⋮ Nonlinear maps preserving condition spectrum of Jordan skew triple product of operators ⋮ Additive maps preserving operator–eigenvector relations ⋮ Nonlinear preservers problem of complex symmetric operators ⋮ Maps preserving fixed points of generalized product of operators

Cites Work

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• On the invariant subspace problem for Banach spaces
• The hyperinvariant subspace lattice of a linear transformation
• A Solution to the Invariant Subspace Problem

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