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Jordan ( α , β ) derivations on triangular algebras and related mappings
Jordan ( α , β ) derivations on triangular algebras and related mappings,10.1016/j.laa.2010.08.018,Linear Algebra and Its Applications,Dong Han,Feng
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Jordan ( α , β ) derivations on triangular algebras and related mappings
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Citations: 2
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Dong Han
,
Feng Wei
Let R be a 2torsion free
commutative ring
with identity, A,B be unital algebras over R and M be a unital (A,B)bimodule, which is faithful as a left Amodule and also as a right Bmodule. Let T=AM0B be the triangular algebra consisting of A,B and M, and let d be an Rlinear mapping from T into itself. Suppose that A and B have only trivial idempotents. Then the following statements are equivalent: (1) d is a Jordan (α,β)derivation on T; (2) d is a Jordan triple (α,β)derivation on T; (3) d is an (α,β)derivation on T. Furthermore, a generalized version of this result is also given. We characterize the actions of automorphisms and skew derivations on the triangular algebra T. The structure of continuous (α,β)derivations of triangular Banach algebras and that of generalized Jordan (α,β)derivations of upper triangular matrix algebras are described.
Journal:
Linear Algebra and Its Applications  LINEAR ALGEBRA APPL
, vol. 434, no. 1, pp. 259284, 2011
DOI:
10.1016/j.laa.2010.08.018
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Citation Context
(1)
...Han and Wei
8
introduced the conceptions of (generalized) (α, β) derivation and (generalized) Jordan (α, β) derivation...
Wenlei Yang
,
et al.
Characterizations of additive (generalized) ξLie (α, β) derivations o...
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Citations
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Characterizations of additive (generalized) ξLie (α, β) derivations on triangular algebras
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