Reflexivity of convex subsets of L(H) and subspaces of \(l^ p\)
type: Item
instance of: scholarly article
title: Reflexivity of convex subsets of L(H) and subspaces of \(l^ p\)
zbMATH Open document ID: 0744.47041
DOI: 10.1155/S0161171291000054
author: Hasan A. Shehada
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1992-06-25T00:00:00Z
full work available at URL: https://eudml.org/doc/46681
review text: Let \(H\) be a Hilbert space and \(S\) a convex subset of \(L(H)\). By the Hahn-Banach theorem, \(S\) is weak\(^{*}\) closed if and only if each \(u\not\in S\) can be separated fraom \(S\) be a nuclear operator via trace duality. In this paper, \(S\) is called \(k\)-reflexive if one can always pick an operator of rank \(\leq k\) to separate \(u\) from \(S\). The author studies \(k\)-reflexive convex sets; his results are a bit too technical to be reproduced here.
Mathematics Subject Classification ID: 47L07
Mathematics Subject Classification ID: 47L05
Mathematics Subject Classification ID: 52A07
Mathematics Subject Classification ID: 47D99
zbMATH DE Number: 7764
zbMATH Keywords: convex subset
zbMATH Keywords: Hahn-Banach theorem
zbMATH Keywords: \(k\)-reflexive convex sets
reviewed by: Dirk Werner
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 7764