Showing papers on "Dual norm published in 1993"
TL;DR: In this article, it was shown that a weak-star upper semi-continuous map with arbitrary non-empty values from a metric space T to the dual X * of an Asplund Banach space X has a selector of the first Baire class to the norm.
61 citations
52 citations
TL;DR: In this paper, it was shown that if the dentability index δ(X) of a Banach space X is less than ω 1 (first uncountable ordinal), then X admits an equivalent locally uniformly convex norm.
Abstract: We prove that if the dentability index δ(X) of a Banach space X is less than ω1 (first uncountable ordinal), then X admits an equivalent locally uniformly convex norm. We prove also that if its weak∗ dentability index δ∗(X) is less than ω1, then X admits an equivalent norm whose dual norm is locally uniformly convex. (∗) : This research has been supported by a grant “Lavoisier” from the french “Ministere des Affaires Etrangeres”.
44 citations
7 citations
6 citations
TL;DR: In this paper, it was shown that the spectral norm of a block matrix is equal to the trace norm of A if and only if A is normal and 1 =w *(A)/n = ∥A∞∞ (the spectral norm) if A was unitarily similar to a block matrices on where A 13 A 22 are unitary and ∥ A 31∥∞≤1.
Abstract: There are several inequalities comparing the numerical radius w(·)(or it's dual norm w *(⋅)) with other norms on Mn , the space of all n×n complex matrices. We give conditions for the case of equality in these inequalities. In particular, we show that w *(A) =∥A∥1 (the trace norm of A) if and only if A is normal and 1=w *(A)/n=∥A∥∞ (the spectral norm of A) if and only if A is unitarily similar to a block matrix on where A 13 A 22 are unitary and ∥A 31∥∞≤1. Moreover we characterize matrices A that satisfy the equality w *(A) =2∥A∥1.
3 citations
30 Apr 1993
TL;DR: In this paper, the authors studied the problem of minimizing the norm, the norm of the inverse and the condition number with respect to the spectral norm, when a submatrix of a matrix can be chosen arbitrarily.
Abstract: : We study the problem of minimizing the norm, the norm of the inverse and the condition number with respect to the spectral norm, when a submatrix of a matrix can be chosen arbitrarily For the norm minimization problem we give a different proof than that given by Davis/Kahan/Weinberger This new approach can then also be used to characterize the completions that minimize the norm of the inverse For the problem of optimizing the condition number we give a partial result Condition number, Norm of a matrix, Matrix completion, Dilation theory, Robust regularization of descriptor systems
1 citations
01 Mar 1993
TL;DR: In this article, it was shown that the images of the entropy norm spaces in Re//1 do not include all of that space and Dabrowski introduced certain natural multiplier operators which map from the entropynorm spaces of B.R. Korenblum into the Hardy space Re/1.
Abstract: R. Dabrowski introduced certain natural multiplier operators which map from the entropy norm spaces of B. Korenblum into the Hardy space Re//1. We show that the images of the entropy norm spaces in Re//1 do not include all of that space.