Norming subspaces, biorthogonal systems, and preconjugate banach spaces

1982 ◽  
Vol 23 (1) ◽  
pp. 33-36 ◽  
Author(s):  
B. V. Godun ◽  
M. I. Kadets
Keyword(s):  
Banach Spaces ◽  
Biorthogonal Systems

On the Cones Associated with Biorthogonal Systems and Bases in Banach Spaces

1969 ◽  
Vol 21 ◽  
pp. 1206-1217 ◽  
Author(s):  
C. W. Mcarthur ◽  
Ivan Singer ◽  
Mark Levin
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Biorthogonal System ◽  
Biorthogonal Systems ◽  
Image Position

1. Let E be a Banach space (by this we shall mean, for simplicity, a real Banach space) and (xn,fn) ({xn} ⊂ E, {fn} ⊂ E*) a biorthogonal system, such that {fn} is total on E (i.e. the relations x ∈ E,fn(x) = 0, n = 1, 2, …, imply x = 0). Then it is natural to consider the cone1which we shall call “the cone associated with the biorthogonal system (xn,fn)”. In particular, if {xn} is a basis of E and {fn} the sequence of coefficient functional associated with the basis {xn}, this cone is nothing else but2and we shall call it “the cone associated with the basis {xn}”.

scholarly journals On biorthogonal systems and Maxur's intersection property

2004 ◽  
Vol 69 (1) ◽  
pp. 107-111 ◽  
Author(s):  
Jan Rychtář
Keyword(s):  
Banach Spaces ◽  
Intersection Property ◽  
Sufficient Condition ◽  
Biorthogonal Systems ◽  
Markushevich Basis ◽  
Mazur's Intersection Property

We give a characterisation of Banach spaces X containing a subspace with a shrinking Markushevich basis {xγ, fγ}γ∈Γ. This gives a sufficient condition for X to have a renorming with Mazur's intersection property.

Biorthogonal Systems in Weakly Lindelöf Spaces

2005 ◽  
Vol 48 (1) ◽  
pp. 69-79
Author(s):  
M. Fabian ◽  
V. Montesinos ◽  
V. Zizler
Keyword(s):  
Banach Spaces ◽  
Biorthogonal Systems

AbstractWe study countable splitting of Markushevich bases in weakly Lindelöf Banach spaces in connection with the geometry of these spaces.

Boundedness of biorthogonal systems in Banach spaces

2010 ◽  
Vol 177 (1) ◽  
pp. 145-154 ◽  
Author(s):  
Petr Hájek ◽  
Vicente Montesinos
Keyword(s):  
Banach Spaces ◽  
Biorthogonal Systems

scholarly journals Biorthogonal systems in Banach spaces

2004 ◽  
Vol 165 (1) ◽  
pp. 81-100
Author(s):  
Michael A. Coco
Keyword(s):  
Banach Spaces ◽  
Biorthogonal Systems

scholarly journals Greedy approximation for biorthogonal systems in quasi-Banach spaces

2021 ◽  
Author(s):  
Fernando Albiac ◽  
José L. Ansorena ◽  
Pablo M. Berná ◽  
Przemysław Wojtaszczyk
Keyword(s):  
Banach Spaces ◽  
Biorthogonal Systems ◽  
Greedy Approximation
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