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Weighted semigroup measure algebra as a WAP-algebra H.R. Ebrahimi Vishki, B. Khodsiani, A. Rejali
... is bounded below, is called a WAP-algebra. When A is either Arens regular or a dual Banach algebra, then natural embedding of A into W AP (A)∗ is an isometry [16, Corollary 4.6]. It has also known that A is a WAP-algebra if and only if it admits an isomorphic representation on a reflexive Banach spac ...
... is bounded below, is called a WAP-algebra. When A is either Arens regular or a dual Banach algebra, then natural embedding of A into W AP (A)∗ is an isometry [16, Corollary 4.6]. It has also known that A is a WAP-algebra if and only if it admits an isomorphic representation on a reflexive Banach spac ...
Chapter 6 Orthogonal representations II: Minimal dimension - D-MATH
... The first non-degeneracy condition we study is general position: we assume that any d of the representing vectors in Rd are linearly independent. A result of Lovász, Saks and Schrijver [6] finds an exact condition for this type of geometric representability. Theorem 1.2 A graph with n nodes has a g ...
... The first non-degeneracy condition we study is general position: we assume that any d of the representing vectors in Rd are linearly independent. A result of Lovász, Saks and Schrijver [6] finds an exact condition for this type of geometric representability. Theorem 1.2 A graph with n nodes has a g ...
the usual castelnuovo s argument and special subhomaloidal
... �ber of the associated rational map is a linear projective space. It is said special if the base locus scheme of the linear system is a smooth irreducible subvariety X ⊂ Pr . Special (sub)homaloidal systems of quadrics deserved great interest. Well known examples are given by quadrics through a rati ...
... �ber of the associated rational map is a linear projective space. It is said special if the base locus scheme of the linear system is a smooth irreducible subvariety X ⊂ Pr . Special (sub)homaloidal systems of quadrics deserved great interest. Well known examples are given by quadrics through a rati ...
Simple Lie algebras having extremal elements
... there are y, h E L such that x, y, h is an 5[2-triple. Moreover, for each such a triple, ad, is diagonizable with eigenvalues 0, ±l, ±2 and satisfies L-2( -adh) = lFx and L2 (-adh) = lFy. Proof. As x is not a sandwich and the characteristic of IF is not 2, there is w E L with !x(w) = -2. By Proposit ...
... there are y, h E L such that x, y, h is an 5[2-triple. Moreover, for each such a triple, ad, is diagonizable with eigenvalues 0, ±l, ±2 and satisfies L-2( -adh) = lFx and L2 (-adh) = lFy. Proof. As x is not a sandwich and the characteristic of IF is not 2, there is w E L with !x(w) = -2. By Proposit ...
Linear algebra
Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.The set of points with coordinates that satisfy a linear equation forms a hyperplane in an n-dimensional space. The conditions under which a set of n hyperplanes intersect in a single point is an important focus of study in linear algebra. Such an investigation is initially motivated by a system of linear equations containing several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations.Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, computer animation, and the social sciences (particularly in economics). Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear models.