Some properties of basic sequences in Banach spaces.
Manuel Valdivia (1997)
Revista Matemática de la Universidad Complutense de Madrid
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Displaying similar documents to “On the existence of fundamental and total founded biorthogonal systems in Banach spaces”
Some properties of basic sequences in Banach spaces.
A note on weakly Lindelöf determined Banach spaces
A. González, Vicente Montesinos (2009)
Czechoslovak Mathematical Journal
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We prove that weakly Lindelöf determined Banach spaces are characterized by the existence of a ``full'' projectional generator. Some other results pertaining to this class of Banach spaces are given.
Complemented and uncomplemented subspaces of Banach spaces.
Anatolij M. Plichko, David Yost (2000)
Extracta Mathematicae
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Does a given Banach space have any non-trivial complemented subspaces? Usually, the answer is: yes, quite a lot. Sometimes the answer is: no, none at all.
The dual of every Asplund space admits a projectional resolution of the identity
Marián Fabian, Gilles Godefroy (1988)
Studia Mathematica
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On strong M-bases in Banach spaces with PRI.
Deba P. Sinha (2000)
Collectanea Mathematica
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If every member of a class P of Banach spaces has a projectional resolution of the identity such that certain subspaces arising out of this resolution are also in the class P, then it is proved that every Banach space in P has a strong M-basis. Consequently, every weakly countably determined space, the dual of every Asplund space, every Banach space with an M-basis such that the dual unit ball is weak* angelic and every C(K) space for a Valdivia compact set K , has a strong M-basis. ...
A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces
G. Androulakis (1998)
Studia Mathematica
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Let (x_n) be a sequence in a Banach space X which does not converge in norm, and let E be an isomorphically precisely norming set for X such that (*) ∑_n |x*(x_{n+1} - x_n)| < ∞, ∀x* ∈ E. Then there exists a subsequence of (x_n) which spans an isomorphically polyhedral Banach space. It follows immediately from results of V. Fonf that the converse is also true: If Y is a separable isomorphically polyhedral Banach space then there exists a normalized M-basis (x_n) which spans Y and...
The existence in every separable Banach space of a fundamental total and bounded biorthogonal sequence and related constructions of uniformly bounded orthonormal systems in
R. I. Ovsepian, A. Pełczyński (1973-1974)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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Separable quotients of Banach spaces.
Jorge Mújica (1997)
Revista Matemática de la Universidad Complutense de Madrid
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In this survey we show that the separable quotient problem for Banach spaces is equivalent to several other problems for Banach space theory. We give also several partial solutions to the problem.