Results 11 to 20 of about 72 (43)

Generalized Lie derivations of unital algebras with idempotents

, 2018
Let A be a unital algebra with a nontrivial idempotent e over a unital commutative ring R . We show that under suitable assumptions every generalized Lie n -derivation F : A → A is of the form F(x) = λx+ Δ(x) , where λ ∈ Z(A ) and Δ is a Lie n ...
Dominik Benkovič
semanticscholar   +1 more source

Strong commutativity preserving maps on triangular rings

, 2012
Let U = Tri(A ,M ,B) be a triangular ring. It is shown, under some mild assumption, that every surjective strong commutativity preserving map Φ : U →U (i.e. [Φ(T ),Φ(S)]= [T,S] for all T,S ∈ U ) is of the form Φ(T ) = ZT + f (T ) , where Z is in Z (U ) ,
X. Qi, J. Hou
semanticscholar   +1 more source

All-derivable subsets for nest algebras on Banach spaces

, 2014
Let N be a nest on a complex Banach space X and let AlgN be the associated nest algebra. We say that a subset S ⊂ AlgN is an all-derivable subset of AlgN if every linear map δ from AlgN into itself derivable on S (i.e. δ satisfies that, for each Z ∈ S, δ(
Yanfang Zhang, J. Hou, X. Qi
semanticscholar   +1 more source

Jordan left derivations and some left derivable maps

, 2010
Let A be an algebra and M be a left A -module. We say that a linear mapping φ : A → M is a left derivable mapping at P if φ(ST ) = Sφ(T ) +Tφ(S) for any S,T ∈ A with ST = P .
Jiankui Li, Jiren Zhou
semanticscholar   +1 more source

Strong commutativity preserving generalized derivations on triangular rings

, 2014
Let U = Tri(A,M,B) be a triangular ring such that either A or B has no nonzero central ideals. It is shown that every pair of strong commutativity preserving generalized derivations g1,g2 of U (i.e., [g1(x),g2(y)] = [x,y] for all x,y ∈U ) is of the form ...
He Yuan, Yao Wang, Yu Wang, Yiqiu Du
semanticscholar   +1 more source

All-derivable points of nest algebras on Banach spaces

, 2012
Let N be a nest on a real or complex Banach space X and let AlgN be the associated nest algebra. Ω ∈ AlgN is called an additively all-derivable point if for any additive map δ : AlgN →AlgN , δ (AB) = δ (A)B+Aδ (B) holds for any A,B ∈ AlgN with AB = Ω ...
Weishun Xue, J. Hou
semanticscholar   +1 more source

Operator Algebras with Unique Preduals [PDF]

Can. Math. Bull. 54 (2011) 411-421, 2008
We show that every free semigroup algebras has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak*-closed unital operator operator algebra containing a weak* dense subalgebra of compact operators has a unique Banach space predual.
arxiv   +1 more source

Single elements of finite CSL algebras

, 2000
An element s of an (abstract) algebra A is a single element of A if asb = 0 and a, b ∈ A imply that as = 0 or sb = 0. Let X be a real or complex reflexive Banach space, and let B be a finite atomic Boolean subspace lattice on X, with the property that ...
W. E. Longstaff, Oreste Panaia
semanticscholar   +1 more source

On the uniqueness of AF diagonals in regular limit algebras [PDF]

arXiv, 2000
Necessary and sufficient conditions are obtained for the uniqueness of standard regular AF masas in regular limit algebras up to approximate inner unitary equivalence.
arxiv  

Topological Radicals of Nest Algebras [PDF]

arXiv, 2016
Let N be a nest on a Hilbert space H and AlgN the corresponding nest algebra. We determine the hypocompact radical of AlgN . Other topological radicals are also characterized.
arxiv