On shrinking basic sequences in Banach spaces
David Dean, Ivan Singer, Leonard Stembach (1971)
Studia Mathematica
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Displaying similar documents to “Quotients with a shrinking basis”
On shrinking basic sequences in Banach spaces
Characterising subspaces of Banach spaces with a Schauder basis having the shift property
Christian Rosendal (2011)
Studia Mathematica
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We give an intrinsic characterisation of the separable reflexive Banach spaces that embed into separable reflexive spaces with an unconditional basis all of whose normalised block sequences with the same growth rate are equivalent. This uses methods of E. Odell and T. Schlumprecht.
Biorthogonal systems and bases in Banach space (Preliminary note)
Jiří Vaníček (1960)
Commentationes Mathematicae Universitatis Carolinae
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A simple proof of two theorems concerning bases of
G. Schechtman (1978-1979)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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Approximation properties and universal Banach spaces
Przemyslaw Wojtaszczyk (1972)
Mémoires de la Société Mathématique de France
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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. ...
On subspaces of locally convex spaces with unconditional Schauder bases
L. Drewnowski (1987)
Colloquium Mathematicae
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Aspects of unconditionality of bases in spaces of compact operators
James R. Holub (1998)
Annales Polonici Mathematici
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E. Tutaj has introduced classes of Schauder bases termed "unconditional-like" (UL) and "unconditional-like*" (UL*) whose intersection is the class of unconditional bases. In view of this association with unconditional bases, it is interesting to note that there exist Banach spaces which have no unconditional basis and yet have a basis of one of these two types (e.g., the space 𝓞[0,1]). In the same spirit, we show in this paper that the space of all compact operators on a reflexive Banach...