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The structure of Lie derivations on C*-algebras
We prove that every Lie derivation on a C � -algebra is in standard form, that is, it can be
The Noncommutative Singer–Wermer Conjecture and ϕ-Derivations
The question of when a $\phi$ -derivation on a Banach algebra has quasinilpotent values, and how this question is related to the noncommutative Singer–Wermer conjecture, is discussed.
Characterizing homomorphisms and derivations on C*-algebras
The main theorem states that a bounded linear operator $h$ from a unital $C^{\ast}$-algebra $A$ into a unital Banach algebra $B$ must be a homomorphism provided that $h(\bm{1})=\bm{1}$ and theExpand
Approximately zero-product-preserving maps
A continuous linear map T from a Banach algebra A into another B approximately preserves the zero products if ‖T(a)T(b)‖ ≤ α‖a‖‖b‖ (a,b ∈ A, ab = 0) for some small positive α. This paper is mainlyExpand
Approximately spectrum-preserving maps
Let X and Y be superreflexive complex Banach spaces and let B(X) and B(Y) be the Banach algebras of all bounded linear operators on X and Y, respectively. If a bijective linear map Φ:B(X)→B(Y) almostExpand
Derivations on Banach Pairs
Essentially defined derivations on semisimple Banach algebras
We prove that every partially defined derivation on a semisimple complex Banach algebra whose domain is a (non necessarily closed) essential ideal is closable. In particular, we show that everyExpand
Characterizing Jordan maps on C*-algebras through zero products
Abstract Let A and B be C*-algebras, let X be an essential Banach A-bimodule and let T : A → B and S : A → X be continuous linear maps with T surjective. Suppose that T(a)T(b) + T(b)T(a) = 0 andExpand
Continuity of Lie derivations on Banach algebras
The Lie structure induced on a Banach algebra by the bracket [a, b] — ab — ba is of lively interest for their intimate connections with the geometry of manifolds modeled on Banach spaces. ManyExpand