Basic and quasibasic subspaces in dual Banach spaces
type: Item
instance of: scholarly article
title: Basic and quasibasic subspaces in dual Banach spaces
zbMATH Open document ID: 0723.46005
DOI: 10.1007/BF01170890
published in: Mathematical Notes
publication date: 1990-01-01T00:00:00Z
review text: Let X be a Banach space and \(X^*\) be its dual. A subspace \(M\subset X^*\) is said to be quasi-basic if it contains all biorthogonal functionals of some (linear) operational basis of X. A subspace \(M\subset X^*\) is said to be basic if it contains all biorthogonal functionals of some basis of X. The existence of spaces with a basis the duals of which contain quasi- basic subspaces which are not basic is proved. The examples of such spaces are \(\ell_ 1\), \(L_ 1(0,1)\).
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 4192396
zbMATH Keywords: quasi-basic
zbMATH Keywords: biorthogonal functionals
zbMATH Keywords: operational basis
author: Mikhail Ostrovskii
MaRDI profile type: Publication
cites work: Q4136031
cites work: Q3810382
description: scientific article; zbMATH DE number 4192396