Results 31 to 40 of about 72 (43)

Lie Biderivations on Triangular Algebras [PDF]

arXiv, 2020
Let $\mathcal{T}$ be a triangular algebra over a commutative ring $\mathcal{R}$ and $\varphi: \mathcal{T} \times \mathcal{T}\longrightarrow \mathcal{T}$ be an arbitrary Lie biderivation of $\mathcal{T}$. We will address the question of describing the form of $\varphi$ in the current work.
arxiv  

Lie Triple Derivations of Incidence Algebras [PDF]

arXiv, 2019
Let $\mathcal{R}$ be a $2$-torsion free commutative ring with unity, $X$ a locally finite pre-ordered set and $I(X,\mathcal{R})$ the incidence algebra of $X$ over $\mathcal{R}$. If $X$ consists of a finite number of connected components, we prove in this paper that every Lie triple derivation of $I(X,\mathcal{R})$ is proper.
arxiv  

Lie-type Derivations of Finitary Incidence Algebras [PDF]

arXiv, 2019
Let $P$ be an arbitrary partially ordered set, $R$ a commutative ring with identity and $FI(P,R)$ the finitary incidence algebra of $P$ over $R$. Under some natural assumption on $R$, we prove that each Lie-type derivation of $FI(P,R)$ is proper.
arxiv  

Limits of Finite Dimensional Nest Algebras [PDF]

arXiv, 2000
We introduce order conserving embeddings as a more general form of order preserving embeddings between finite dimensional nest algebras. The structure of these embeddings is determined, in terms of order indecomposable decompositions, and they are shown to be determined up to inner conjugacy by their induced maps on $K_0$.
arxiv  

Decompositions of Reflexive Bimodules over Maximal Abelian Selfadjoint Algebras [PDF]

arXiv, 2004
We generalize the notion of `diagonal' from the class of CSL algebras to masa bimodules. We prove that a reflexive masa bimodule decomposes as a sum of two bimodules, the diagonal and a module generalizing the w*-closure of the Jacobson radical of a CSL algebra.
arxiv  

Rank Preserving Maps on CSL Algebras [PDF]

arXiv, 2006
We give a description of a weakly continuous rank preserving map on a reflexive algebra on complex Hilbert space with commutative completely distributive subspace lattice. We show that the implementation of a rank preserving map can be described by the combination of two different types of maps.
arxiv  

Generalized homomorphisms and KK with extra structure [PDF]

arXiv
We develop the approach via quasihomomorphisms and the universal algebra $qA$ to Kasparov's $KK$-theory, so as to cover versions of $KK$ such as $KK^{nuc}$, $KK^G$ and ideal related $KK$-theory.
arxiv  

Projections and idempotents with fixed diagonal and the homotopy problem for unit tight frames [PDF]

Operators and Matrices 5 (2011), no. 1, 139-155, 2009
We investigate the topological and metric structure of the set of idempotent operators and projections which have prescribed diagonal entries with respect to a fixed orthonormal basis of a Hilbert space. As an application, we settle some cases of conjectures of Larson, Dykema, and Strawn on the connectedness of the set of unit-norm tight frames.
arxiv  

Additive Lie ($ξ$-Lie) Derivations and Generalized Lie ($ξ$-Lie) Derivations on Prime Algebras [PDF]

arXiv, 2010
The additive (generalized) $\xi$-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumption, that an additive map $L$ is an additive (generalized) Lie derivation if and only if it is the sum of an additive (generalized) derivation and an additive map from the algebra into its center vanishing all commutators; is an
arxiv  

Jordan derivations on triangular matrix rings [PDF]

arXiv, 2014
Guided by the research line introduced by Martindale III in [1] on the study of the additivity of maps, this article aims establish condi- tions on triangular matrix rings in order that an map ' satisfying '(ab + ba) = '(a)b + a'(b) + '(b)a + b'(a) for all a; b in a triangular matrix ring becomes additive.
arxiv