A condition for a subspace of \({\mathcal B} (H)\) to be an ideal

DOI10.1016/0024-3795(94)00143-XzbMath0852.46021MaRDI QIDQ1911933

Lajos Molnár

Publication date: 28 April 1996

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

zbMATH Keywords

ideal

Mathematics Subject Classification ID

Spaces of operators; tensor products; approximation properties (46B28) Algebras of operators on Banach spaces and other topological linear spaces (47L10)

Related Items (51)

Maps preserving product \(A^\ast B + B^\ast A\) on \(C^\ast\)-algebras ⋮ Mixed *-Jordan-type derivations on *-algebras ⋮ Nonlinear maps preserving the Jordan triple *-product on factor von Neumann algebras ⋮ Strong skew commutativity preserving maps on rings with involution. ⋮ Nonlinear skew Jordan derivable maps on factor von Neumann algebras ⋮ Nonlinear skew Lie triple derivations between factors ⋮ Nonlinear mappings preserving Jordan-type \(\eta\)-\(\ast\)-products ⋮ Nonlinear \(*\)-Lie \(n\)-tuple derivations on prime \(*\)-algebras ⋮ Maps preserving product \(A^* B + BA^*\) on \(C^*\)-algebras ⋮ Nonlinear \(\ast\)-Jordan triple derivation on prime \(\ast\)-algebras ⋮ Maps preserving the bi-skew Jordan product on factor von Neumann algebras ⋮ Maps preserving n-tuple A*B − B*A derivations on factor von Neumann algebras ⋮ Maps preserving \(A^*A+AA^*\) on \(C^*\)-algebras ⋮ Strong bi-skew commutativity preserving maps on von Neumann algebras ⋮ Nonlinear mappings preserving product \(XY+YX^\ast\) on factor von Neumann algebras ⋮ Nonlinear triple product \(A^*B + B^*A\) for derivations on \(\ast \)-algebras ⋮ Strong 3-skew commutativity preserving maps on prime rings with involution ⋮ Nonlinear maps preserving the Jordan triple \(\ast\)-product between factors ⋮ A note on strong skew Jordan product preserving maps on von Neumann algebras ⋮ Maps preserving products \(XY - YX^*\) on von Neumann algebras ⋮ Strong 2-skew commutativity preserving maps on prime rings with involution ⋮ Additivity of maps preserving productsAP±PA^*onC^*-algebras ⋮ Equivalent characterization of ∗-derivations on von Neumann algebras ⋮ Spectrum and local spectrum preservers of skew Lie products of matrices ⋮ Recent progress on local spectrum-preserving maps ⋮ A note on strong (skew) η-Lie products preserving maps on some algebras ⋮ Nonlinear \(*\)-Jordan-type derivations on \(*\)-algebras ⋮ Multiplicative ∗-Jordan type higher derivations on von Neumann algebras ⋮ Nonlinear *-Lie-type derivations on standard operator algebras ⋮ Nonlinear maps preserving the Jordan triple 1-\(*\)-product on von Neumann algebras ⋮ Multiplicative *-Lie type higher derivations of standard operator algebras ⋮ A note on strong \(\eta \)-Lie products preserving maps on some algebras ⋮ Some unitary similarity invariant sets preservers of skew Lie products ⋮ Non-linear \(\lambda\)-Jordan triple \(\ast\)-derivation on prime \(\ast\)-algebras ⋮ Nonlinear maps preserving Jordan \(\ast\)-products ⋮ Nonlinear mappings preserving Jordan multiple ∗– product on factor von Neumann algebras ⋮ k-skew Lie products on prime rings with involution ⋮ Strong skew commutativity preserving maps on von Neumann algebras ⋮ Non-linear *-Jordan derivations on von Neumann algebras ⋮ STRONG SKEW COMMUTATIVITY PRESERVING MAPS ON RINGS ⋮ Multiplicative ∗-lie triple higher derivations of standard operator algebras ⋮ A characterization of \(*\)-automorphism on \({\mathcal B}(H)\) ⋮ Nonlinear maps preserving higher-dimensional numerical ranges of Jordan \(*\)-products ⋮ Strong (skew) ξ-Lie commutativity preserving maps on algebras ⋮ Non-linear new product A*B-B*A derivations on *-algebras ⋮ Properties and preservers of numerical radius on skew Lie products of operators ⋮ Maps preserving product \(XY -YX^*\) on factor von Neumann algebras ⋮ Non-linear ξ-Jordan *-derivations on von Neumann algebras ⋮ On maps preserving zeros of the polynomial \(xy - yx^\ast\) ⋮ Nonlinear skew commuting maps on \(*\)-rings ⋮ A note on nonlinear skew Lie triple derivation between Prime $\ast$-algebras

Cites Work

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• Jordan *-derivation pairs and quadratic functionals on modules over *-rings
• Ring derivations on standard operator algebras
• On Jordan *-derivations and an application
• On the structure of Jordan *-derivations
• Jordan ∗-Derivations of Standard Operator Algebras
• Quadratic and Quasi-Quadratic Functionals
• Lie and Jordan Ideals of Operators on Hilbert Space

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