منابع مشابه
Representations of the Direct Product of Matrix Algebras
Suppose B is the unital algebra consisting of the algebraic product of full matrix algebras over an index set X. A bijection is set up between the equivalence classes of irreducible representations of B as operators on a Banach space and the σ-complete ultrafilters on X, Theorem 2.6. Therefore, if X has less than measurable cardinality (e.g. accessible), the equivalence classes of the irreducib...
متن کاملJordan 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 کاملA Formula for the Direct Product of Crossed Product Algebras
tive radius r. Let the center Xo be the sequence {&?}, and let 5 be chosen so large that 2~~ + 2~ s 2 + • • • k Q s. If we define xi as (ki, &2> ' * • » $j j8+i, is+2, • • • ), then xi belongs to K and limn fn(xi) = + °°Consequently xi cannot be a point of Up and this contradiction establishes U as a set of the f...
متن کاملAbstract structure of partial function $*$-algebras over semi-direct product of locally compact groups
This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism. Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1977
ISSN: 0024-3795
DOI: 10.1016/0024-3795(77)90015-5