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Jordan left {g, h}-derivations over some algebras [PDF]

arXiv, 2018
In this article, left {g, h}-derivation and Jordan left {g, h}-derivation on algebras are introduced. It is shown that there is no Jordan left {g, h}-derivation over $\mathcal{M}_n(C)$ and $\mathbb{H}_{\mathbb{R}}$, for g not equal to h. Examples are given which show that every Jordan left $\{g, h\}$-derivation over $\mathcal{T}_n(C)$, $\mathcal{M}_n(C)
arxiv  

Commuting maps on certain 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, in this paper we give a sufficient and necessary condition for each commuting map on $I(X,\mathcal{R})$ being proper.
arxiv  

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Some Characterizations of Commutative Subspace Lattices

, 2004
Let H be a not necessarily separable Hilbert space, and let BH denote the space of all bounded linear operators on H. It is proved that a commutative lattice D of self‐adjoint projections in H that contains 0 and I is spatially complete if and only if it
D. Edwards
semanticscholar   +1 more source