منابع مشابه
Jordan product determined points in matrix algebras
Let Mn(R) be the algebra of all n×n matrices over a unital commutative ring R with 6 invertible. We say that A ∈ Mn(R) is a Jordan product determined point if for every R-module X and every symmetric R-bilinear map {·, ·} : Mn(R)×Mn(R) → X the following two conditions are equivalent: (i) there exists a fixed element w ∈ X such that {x, y} = w whenever x ◦ y = A, x, y ∈ Mn(R); (ii) there exists ...
متن کاملZero Triple Product Determined Matrix Algebras
Let A be an algebra over a commutative unital ring C. We say that A is zero triple product determined if for every C-module X and every trilinear map {·, ·, ·}, the following holds: if {x, y, z} 0 whenever xyz 0, then there exists a C-linear operator T : A3 −→ X such that {x, y, z} T xyz for all x, y, z ∈ A. If the ordinary triple product in the aforementioned definition is replaced by Jordan t...
متن کاملOn strongly Jordan zero-product preserving maps
In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...
متن کاملon strongly jordan zero-product preserving maps
in this paper, we give a characterization of strongly jordan zero-product preserving maps on normed algebras as a generalization of jordan zero-product preserving maps. in this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly jordan zero-product preserving maps are completely different. also, we prove that the direct p...
متن کاملZero Product Preservers of C*-algebras
Let θ : A → B be a zero-product preserving bounded linear map between C*-algebras. Here neither A nor B is necessarily unital. In this note, we investigate when θ gives rise to a Jordan homomorphism. In particular, we show that A and B are isomorphic as Jordan algebras if θ is bijective and sends zero products of self-adjoint elements to zero products. They are isomorphic as C*-algebras if θ is...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2015
ISSN: 0024-3795
DOI: 10.1016/j.laa.2015.01.035