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The Jordan structure of CSL algebras

100%
Lu F.
Studia Mathematica
|
2009
|
tom 190
|
nr 3
283-299
EN
We show that every Jordan isomorphism between CSL algebras is the sum of an isomorphism and an anti-isomorphism. Also we show that each Jordan derivation of a CSL algebra is a derivation.
2
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Similarity-preserving linear maps on B(X)

63%
Lu F., Peng C.
Studia Mathematica
|
2012
|
tom 209
|
nr 1
1-10
EN
Let X be an infinite-dimensional Banach space, and B(X) the algebra of all bounded linear operators on X. Then ϕ: B(X) → B(X) is a bijective similarity-preserving linear map if and only if one of the following holds: (1) There exist a nonzero complex number c, an invertible bounded operator T in B(X) and a similarity-invariant linear functional h on B(X) with h(I) ≠ -c such that $ϕ(A) = cTAT^{-1} + h(A)I$ for all A ∈ B(X). (2) There exist a nonzero complex number c, an invertible bounded linear operator T: X* → X and a similarity-invariant linear functional h on B(X) with h(I) ≠ -c such that $ϕ(A) = cTA*T^{-1} + h(A)I$ for all A ∈ B(X).
3
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Algebraic isomorphisms and Jordan derivations of 𝒥-subspace lattice algebras

63%
Lu F., Li P.
Studia Mathematica
|
2003
|
tom 158
|
nr 3
287-301
EN
It is shown that every algebraic isomorphism between standard subalgebras of 𝒥-subspace lattice algebras is quasi-spatial and every Jordan derivation of standard subalgebras of 𝒥-subspace lattice algebras is an additive derivation. Also, it is proved that every finite rank operator in a 𝒥-subspace lattice algebra can be written as a finite sum of rank one operators each belonging to that algebra. As an additional result, a multiplicative bijection of a 𝒥-subspace lattice algebra onto an arbitrary ring is proved to be automatically additive. Those results can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.
4
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2-local Lie isomorphisms of operator algebras on Banach spaces

51%
Chen L., Huang L., Lu F.
Studia Mathematica
|
2015
|
tom 229
|
nr 1
1-11
EN
Let X and Y be complex Banach spaces of dimension greater than 2. We show that every 2-local Lie isomorphism ϕ of B(X) onto B(Y) has the form ϕ = φ + τ, where φ is an isomorphism or the negative of an anti-isomorphism of B(X) onto B(Y), and τ is a homogeneous map from B(X) into ℂI vanishing on all finite sums of commutators.
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