Search results for "Linear form"
showing 10 items of 47 documents
On the Bishop–Phelps–Bollobás theorem for multilinear mappings
2017
Abstract We study the Bishop–Phelps–Bollobas property and the Bishop–Phelps–Bollobas property for numerical radius. Our main aim is to extend some known results about norm or numerical radius attaining operators to multilinear and polynomial cases. We characterize the pair ( l 1 ( X ) , Y ) to have the BPBp for bilinear forms and prove that on L 1 ( μ ) the numerical radius and the norm of a multilinear mapping are the same. We also show that L 1 ( μ ) fails the BPBp-nu for multilinear mappings although L 1 ( μ ) satisfies it in the operator case for every measure μ.
Partial *-algebras of closable operators: A review
1996
This paper reviews the theory of partial *-algebras of closable operators in Hilbert space (partial O*-algebras), with some emphasis on partial GW*-algebras. First we discuss the general properties and the various types of partial *-algebras and partial O*-algebras. Then we summarize the representation theory of partial *-algebras, including a generalized Gel’fand-Naimark-Segal construction; the main tool here is the notion of positive sesquilinear form, that we study in some detail (extendability, normality, order structure, …). Finally we turn to automorphisms and derivations of partial O*-algebras, and their mutual relationship. The central theme here is to find conditions that guarante…
Representable linear functionals on partial *-algebras
2012
A GNS-like *-representation of a partial *-algebra \({{\mathfrak A}}\) defined by certain representable linear functionals on \({{\mathfrak A}}\) is constructed. The study of the interplay with the GNS construction associated with invariant positive sesquilinear forms (ips) leads to the notions of pre-core and of singular form. It is shown that a positive sesquilinear form with pre-core always decomposes into the sum of an ips form and a singular one.
Polynomial identities for the Jordan algebra of a degenerate symmetric bilinear form
2013
Let J(n) be the Jordan algebra of a degenerate symmetric bilinear form. In the first section we classify all possible G-gradings on J(n) where G is any group, while in the second part we restrict our attention to a degenerate symmetric bilinear form of rank n - 1, where n is the dimension of the vector space V defining J(n). We prove that in this case the algebra J(n) is PI-equivalent to the Jordan algebra of a nondegenerate bilinear form.
Convolution of three functions by means of bilinear maps and applications
1999
When dealing with spaces of vector-valued analytic functions there is a natural way to understand multipliers between them. If X and Y are Banach spaces and L(X,Y ) stands for the space of linear and continuous operators we may consider the convolution of L(X,Y )-valued analytic functions, say F (z) = ∑ n=0∞ Tnz , and X-valued polynomials, say f(z) = ∑m n=0 xnz , to get the Y -valued function F ∗ f(z) = ∑ Tn(xn)z. The second author considered such a definition and studied multipliers between H(X) and BMOA(Y ) in [5]. When the functions take values in a Banach algebra A then the natural extension of multiplier is simply that if f(z) = ∑ anz n and g(z) = ∑ bnz , then f ∗ g(z) = ∑ an.bnz n whe…
Approximation of Elliptic Hemivariational Inequalities
1999
From the previous chapter we know that there exist many important problems in mechanics in which constitutive laws are expressed by means of nonmonotone, possibly multivalued relations (nonmonotone multivalued stress-strain or reaction-displacement relations,e.g). The resulting mathematical model leads to an inclusion type problem involving multivalued nonmonotone mappings or to a substationary type problem for a nonsmooth, nonconvex superpotential expressed in terms of calculus of variation. It is the aim of this chapter to give a detailed study of a discretization of such a type of problems including the convergence analysis. Here we follow closely Miettinen and Haslinger, 1995, Miettinen…
Comment on “Topological invariants, instantons, and the chiral anomaly on spaces with torsion”
1999
In Riemann-Cartan spacetimes with torsion only its axial covector piece $A$ couples to massive Dirac fields. Using renormalization group arguments, we show that besides the familiar Riemannian term only the Pontrjagin type four-form $dA\wedge dA$ does arise additionally in the chiral anomaly, but not the Nieh-Yan term $d^\star A$, as has been claimed in a recent paper [PRD 55, 7580 (1997)].
Kronecker modules and reductions of a pair of bilinear forms
2004
We give a short overview on the subject of canonical reduction of a pair of bilinear forms, each being symmetric or alternating, making use of the classification of pairs of linear mappings between vector spaces given by J. Dieudonné.
Analysis of singular bilinear systems using Walsh functions
1991
The use of Walsh functions to analyse singular bilinear systems is investigated. It is shown that the nonlinear implicit differential system equation may be converted to a set of linear algebraic Lyapunov equations to be solved iteratively for the coefficients of the semistate x(t) in terms of the Walsh basis functions. Solution of the iterative algorithm is uniformly convergent to the exact solution of the algebraic generalised Lyapunov equation of the singular bilinear system. The present method is slightly more complicated than a similar one arising from the analysis of linear singular systems. In fact, it is a hybrid between the analyses of usual linear singular and bilinear regular sys…
Counting and equidistribution in Heisenberg groups
2014
We strongly develop the relationship between complex hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on complex hyperbolic spaces, especially in dimension $2$. We prove a Mertens' formula for the integer points over a quadratic imaginary number fields $K$ in the light cone of Hermitian forms, as well as an equidistribution theorem of the set of rational points over $K$ in Heisenberg groups. We give a counting formula for the cubic points over $K$ in the complex projective plane whose Galois conjugates are orthogonal and isotropic for a given Hermitian form over $K$, and a counting and equidistribution result for …