ADDITIVE MAPS ON SOME OPERATOR ALGEBRAS BEHAVING LIKE (alpha, 0)-DERIVATIONS OR GENERALIZED (alpha, 0)-DERIVATIONS AT ZERO-PRODUCT ELEMENTS

作者：Ghahramani Hoger^*

来源：Acta Mathematica Scientia, 2014, 34(4): 1287-1300.

• operator algebra
• nest algebra (alpha, 0)-derivation
• generalized (alpha, 0)-derivation

Let A be a subalgebra of B(X) containing the identity operator I and an idempotent P. Suppose that alpha,beta : A -> A are ring epimorphisms and there exists some nest N on X such that alpha(P)(X) and 0(P)(X) are non-trivial elements of Ai. Let A contain all rank one operators in Alg.AT and delta : A -> B(X) be an additive mapping. It is shown that, if delta is (alpha, beta)-derivable at zero point, then there exists an additive (alpha, beta)-derivation T : A -> B(X) such that delta(A) = tau(A) + alpha(A)delta(I) for all A is an element of A. It is also shown that if 5 is generalized (alpha, beta)-derivable at zero point, then delta is an additive generalized (zeta, beta)-derivation. Moreover, by use of this result, the additive maps (generalized) (alpha, beta)-derivable at zero point on several nest algebras, are also characterized.

• 出版日期2014-7