Showing papers on "Dual norm published in 2001"

ON n-NORMED SPACES

Abstract: Given an n-normed space with n ≥ 2, we offer a simple way to derive an (n−1)- norm from the n-norm and realize that any n-normed space is an (n − 1)-normed space. We also show that, in certain cases, the (n − 1)-norm can be derived from the n-norm in such a way that the convergence and completeness in the n-norm is equivalent to those in the derived (n − 1)-norm. Using this fact, we prove a fixed point theorem for some n-Banach spaces.

The space of p -summable sequences and its natural n -norm

Abstract: We study the space lp, 1 ≤ p ≤ ∞, and its natural n-norm, which can viewed as a generalisation of its usual norm. Using a derived norm equivalent to its usual norm, we show that lp is complete with respect to its natural n-norm. In addition, we also prove a fixed point theorem for lp as an n-normed space.

Inner derivations and norm equality

Abstract: We characterize when the norm of the sum of two bounded operators on a Hilbert space is equal to the sum of their norms.

BV as a dual space

Abstract: Let C be a field of subsets of a set I. It is well known that the space FA of all the finitely additive games of bounded variation on C is the norm dual of the space of all simple functions on C. In this paper we prove that the space BV of all the games of bounded variation on C is the norm dual of the space of all simple games on C. This result is equivalent to the compactness of the unit ball in BV with respect to the vague topology.

A posteriori error estimator for a mixed finite element method for Reissner-Mindlin plate

Abstract: We present an a posteriori error estimator for a mixed finite element method for the Reissner-Mindlin plate model. The finite element method we deal with, was analyzed by Duran and Liberman in 1992 and can also be seen as a particular example of the general family analyzed by Brezzi, Fortin and Stenberg in 1991. The estimator is based on the evaluation of the residual of the finite element solution. We show that the estimator yields local lower and global upper bounds of the error in the numerical solution in a natural norm for the problem, which includes the H 1 norms of the terms corresponding to the deflection and the rotation and a dual norm for the shearing force The estimates are valid uniformly with respect to the plate thickness.

On the norm of the fourier-jacobi projection

Abstract: We extend the results of Pollard [7] and give asymptotic estimates for the norm of the Fourier-Jacobi projection operator in the appropriate weighted Lp space.

Bergman norm estimates of Poisson integrals

Abstract: On the half space Rn × R+, it has been known that harmonic Bergman space bp can contain a positive function only if . Thus, for , Poisson integrals can be bp-functions only by means of their boundary cancellation properties. In this paper, we describe what those cancellation properties explicitly are. Also, given such cancellation properties, we obtain weighted norm inequalities for Poisson integrals. As a consequence, under weighted integrability condition given by our weighted norm inequalities, we show that our cancellation properties are equivalent to the bp-containment of Poisson integrals for p under consideration. Our results are sharp in the sense that orders of our weights cannot be improved.

On a characterisation of inner product spaces

Abstract: It is well known that for the Hilbert space H the minimum value of the functional F"(f) = R H kf igk 2 d"(g); f 2 H; is achived at the mean of " for any probability measure " with strong second moment on H: We show that the validity of this property for measures on a normed space having support at three points with norm 1 and arbitrarily fixed positive weights implies the existence of an inner product that generates the norm.

Norm attaining operators and James’ Theorem

Abstract: There are several results relating isomorphic properties of a Banach space and the set of norm attaining functionals. Here, we show versions for operators of some of these results. For instance, a Banach space X has to be reflexive if it does not contain l1 and for some non trivial Banach space Y and positive r, the unit ball of the space of operators from X into Y is the closure (weak operator topology) of the convex hull of the norm one operators satisfying that balls centered at any of them with radius r are contained in the set of norm attaining operators. We also prove a similar result by using a very weak isometric condition on the space instead of non containing l1.