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The Jordan structure of CSL algebras

Fangyan Lu — 2009

Studia Mathematica

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.

Algebraic isomorphisms and Jordan derivations of 𝒥-subspace lattice algebras

Fangyan LuPengtong Li — 2003

Studia Mathematica

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...

Similarity-preserving linear maps on B(X)

Fangyan LuChaoran Peng — 2012

Studia Mathematica

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 ) = c T A T - 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...

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