Acta mathematica scientia, Series B >
ADDITIVE MAPS ON SOME OPERATOR ALGEBRAS BEHAVING LIKE (α, β)-DERIVATIONS OR GENERALIZED (α, β)-DERIVATIONS AT ZERO-PRODUCT ELEMENTS
Received date: 2012-04-12
Revised date: 2013-12-03
Online published: 2014-07-20
Let A be a subalgebra of B(X) containing the identity operator I and an idem-potent P. Suppose that Let A be a subalgebra of B(X) containing the identity operator I and an idem-potent P. Suppose that α, β : A → A are ring epimorphisms and there exists some nest N on X such that α(P)(X) and β(P)(X) are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ : A →B(X) be an additive mapping. It is shown that, if δ is (α, β)-derivable at zero point, then there exists an additive (α, β)-derivation τ : A →B(X) such that δ(A) =τ (A) + α(A)δ(I) for all A ∈ A. It is also shown that if δ is generalized (α, β)-derivable at zero point, then δis an additive generalized (α, β)-derivation. Moreover,
by use of this result, the additive maps (generalized) (α, β)-derivable at zero point on several nest algebras, are also characterized.
Hoger GHAHRAMANI . ADDITIVE MAPS ON SOME OPERATOR ALGEBRAS BEHAVING LIKE (α, β)-DERIVATIONS OR GENERALIZED (α, β)-DERIVATIONS AT ZERO-PRODUCT ELEMENTS[J]. Acta mathematica scientia, Series B, 2014 , 34(4) : 1287 -1300 . DOI: 10.1016/S0252-9602(14)60085-0
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