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

doi:10.1016/S0252-9602(14)60085-0

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1287-1300.doi: 10.1016/S0252-9602(14)60085-0

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

Hoger GHAHRAMANI

Department of Mathematics, University of Kurdistan, P.O. Box 416, Sanandaj, Iran

收稿日期:2012-04-12 修回日期:2013-12-03 出版日期:2014-07-20 发布日期:2014-07-20

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

Hoger GHAHRAMANI

Department of Mathematics, University of Kurdistan, P.O. Box 416, Sanandaj, Iran

Received:2012-04-12 Revised:2013-12-03 Online:2014-07-20 Published:2014-07-20

摘要/Abstract

摘要：

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.

关键词: operator algebra, nest algebra, (α, β)-derivation, generalized (α, β)-derivation

Abstract:

Key words: operator algebra, nest algebra, (α, β)-derivation, generalized (α, β)-derivation

中图分类号:

47B49

Hoger GHAHRAMANI. ADDITIVE MAPS ON SOME OPERATOR ALGEBRAS BEHAVING LIKE (α, β)-DERIVATIONS OR GENERALIZED (α, β)-DERIVATIONS AT ZERO-PRODUCT ELEMENTS[J]. 数学物理学报(英文版), 2014, 34(4): 1287-1300.

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.

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

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

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