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Note on Derivations of Certain non-CSL Algebras
A subspace lattice \(\{(0), M, N, H\}\) of a Hilbert space
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Inequalities for the Heinz mean of sector matrices involving positive linear maps
In this paper, we present some Heinz mean inequalities for sector matrices involving positive linear maps which generalize the results of Mao et al. Moreover, we give some inequalities involving the mean of in...
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Article
Similarity preserving linear maps on \({\mathscr {J}}\) -subspace lattice algebras
We describe the structure of similarity preserving linear maps of reflexive algebras with \({\mathscr {J}}\) J -subspace lattices. This result can apply to atomic Boolean subspace lattice algebras and pentagon...
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Maps on Idempotent Operators with Infinite-Dimensional Kernel
Let X be an infinite-dimensional Banach space and \(\tau _\infty (X)\)τ∞(X) the set of all bounded linear idempotent operators on X with infinite-dimensional kernel. We give a characterization of three types of m...
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Nonlinear maps preserving higher-dimensional numerical ranges of Jordan \(*\)-products
Let H and K be complex Hilbert spaces. Denote by \(B(H)\)B(H) and \(B(K)\)B(K) the algebras of all bounded linear operators on H and K, respectively. In this paper, we characterize that nonlinear map $$\phi : B(H...
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Local Maps of JSL Algebras
A JSL algebra is a reflexive algebra with the \({\mathcal {J}}\) J ...
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Open AccessSome reverse mean inequalities for operators and matrices
In this paper, we present some new reverse arithmetic–geometric mean inequalities for operators and matrices due to Lin (Stud. Math. 215:187–194, 2013). Among other inequalities, we prove that if ...
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Article
Lie isomorphisms of reflexive algebras. II
By characterizing minimal non-central Lie ideals, we describe the structure of Lie isomorphisms of reflexive algebras with J-subspace lattices. This result can apply to reflexive algebras with atomic Boolean subs...
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Article
Open AccessSome generalizations of inequalities for sector matrices
In this paper, we generalize some Schatten p-norm inequalities for accretive-dissipative matrices obtained by Kittaneh and Sakkijha. Moreover, we present some inequalities for sector matrices.
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Nonlinear Maps Preserving the Jordan Triple 1- \(*\) -Product on Von Neumann Algebras
In this paper, we investigate a bijective map \(\Phi \) Φ ...
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2-Local \({*}\) -Lie isomorphisms of operator algebras
Let \({H}\) H b...
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Reduced Crossed Products Associated with Banach Algebra Dynamical Systems
We define reduced crossed products associated with a Banach algebra dynamical system. If the group is amenable, we prove that the reduced crossed product and the crossed product are isometrically isomorphic.
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Decomposability of Finite Rank Operators in Lie Ideals of Nest Algebras
A set of operators is said to be decomposable if each finite rank operator in it can be written as a sum of finitely many rank-1 operators in it. In this note, we establish a sufficient and necessary condition...
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Article
Local and 2-Local Lie Derivations of Operator Algebras on Banach Spaces
Let X be a Banach space of dimension > 2. We show that every local Lie derivation of B(X) is a Lie derivation, and that a map of B(X) is a 2-local Lie derivation if and only if it has the form
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Linear Maps Preserving Numerical Radius on Nest Algebras
A linear map \({\phi}\) of operator algebras is said to preserve numerical radius (or to be a numerical radius isomet...
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Jordan Derivations of Reflexive Algebras
Let \({\mathcal L}\) be a subspace lattice on a Banach space X and suppose that
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Lie Derivations of Reflexive Algebras
A Lie derivation is called standard if it is a sum of a derivation and a linear map with image in the center vanishing on commutators. In this paper we show that Lie derivations of a reflexive algebra ...
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Weakly closed Jordan ideals in nest algebras on Banach spaces
We show that weakly closed Jordan ideals in nest algebras on Banach spaces are associative ideals. The decomposability of finite-rank operators in Jordan ideals and the commutants of bimodules are also investi...
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Article
Lie and Jordan Ideals in Reflexive Algebras
A CDCSL algebra is a reflexive operator algebra with completely distributive and commutative subspace lattice. In this paper, we show, for a weakly closed linear subspace
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Lie derivations of certain CSL algebras
It is shown that each Lie derivation on a reflexive algebra, whose lattice is completely distributive and commutative, can be uniquely decomposed into the sum of a derivation and a linear map** with image in...
