Showing papers on "Dual norm published in 1989"
01 Mar 1989
TL;DR: In this paper, the authors studied the relationship between Wijsman convergence and Mosco convergence for sequences of convex sets and showed that the underlying space is reflexive with the dual norm having the Kadec property.
Abstract: We study the relationship between Wijsman convergence and Mosco convergence for sequences of convex sets. Our central result is that Mosco convergence and Wijsman convergence coincide for sequences of convex sets if and only if the underlying space is reflexive with the dual norm having the Kadec property.
38 citations
7 citations
Journal Article•
TL;DR: In this paper, the authors considered the Borel.sigma-algebra B(B) of B which satisfies (Fig.) where is the topological dual of B and (.,.) is the natural dual pairing between B and.
Abstract: Let (H, B, .nu.) be an abstract Wiener space where H is a separable Hilbert space with the inner product and the norm vertical bar . vertical bar=.root., which is densely and continuously imbedded into a separable Banach space B with the norm ∥.∥ , and .nu. is a probability measure on the Borel .sigma.-algebra B(B) of B which satisfies (Fig.) where is the topological dual of B and (.,.) is the natural dual pairing between B and . We will regard .contnd.H.contnd.B in the natural way. Thus we have =(y, x) for all y in and x in H. Let and C denote the n-dimensional Euclidean space and the complex numbers respectively.ctively.
2 citations
TL;DR: In this article, it was shown that if a norm has an infinite rigid set, then, up to linear transformation, the norm is Euclidean and the set is a circle.
Abstract: A compact set in the plane is rigid with respect to a norm if the norm isometries of the set act transitively on it. We show that if a norm has an infinite rigid set, then, up to linear transformation, the norm is Euclidean and the set is a circle. Our methods also yield a new characterisation of the ellipse.
2 citations
01 Jan 1989
TL;DR: The following class of spaces is formally larger than the class of weak Asplund spaces, but appears to be a more natural object of study as discussed by the authors, and has been studied extensively in the literature.
Abstract: The following class of spaces is formally larger than the class of weak Asplund spaces, but appears to be a more natural object of study.
1 citations
20 Mar 1989
TL;DR: In this article, it was shown that a Banach function space E on a separable measure space which has the Fatou property is a dual Banach lattice if and only if all positive operators from L 1 (0, 1) into E are abstract kernel operators.
Abstract: In this paper we give a characterization of dual Banach lattices. In fact, we prove that a Banach function space E on a separable measure space which has the Fatou property is a dual Banach lattice if and only if all positive operators from L 1 (0,1) into E are abstract kernel operators, hence extending the fact, proved by M. Talagrand, that separable Banach lattices with the Radon-Nikodym property are dual Banach lattices.
1 citations
01 Jan 1989
TL;DR: In this paper, it was shown that the density p b (x) of the distribution function of a stable random vector in a real, separable Banach space can be estimated in the form Open image in new window, where c is a constant, depending on the geometry of the space.
Abstract: Let Y be a stable random vector in a real, separable Banach space B Suppose that the distribution of Y has infinite dimensional support and the space B has smooth enough norm and B is uniformly convex with power order (see in the paper) We prove that the density p b (x) of the distribution function F b (x)=P{‖Y+b‖
TL;DR: The Norm of a Linear Functional (Norm of Linear Functional Programming) as mentioned in this paper is a linear functional model for linear functional programming. The American Mathematical Monthly: Vol. 96, No. 5, pp. 434-436.
Abstract: (1989). The Norm of a Linear Functional. The American Mathematical Monthly: Vol. 96, No. 5, pp. 434-436.