All separable Banach space admit for every ε>0 fundamental total and bounded by 1 + ε biorthogonal sequences
Almost sure summability of subsequences in Banach spaces
An approach to generalizing Banach spaces: normed almost linear spaces
An estimation of the Lebesgue functions of biorthogonal systems with an application to the non-existence of some bases in C and
An Example Concerning Valdivia Compact Spaces
∗ Supported by Research grants GAUK 190/96 and GAUK 1/1998We prove that the dual unit ball of the space C0 [0, ω1 ) endowed with the weak* topology is not a Valdivia compact. This answers a question posed to the author by V. Zizler and has several consequences. Namely, it yields an example of an affine continuous image of a convex Valdivia compact (in the weak* topology of a dual Banach space) which is not Valdivia, and shows that the property of the dual unit ball being Valdivia is not an isomorphic...
An ordinal version of some applications of the classical interpolation theorem
Let E be a Banach space with a separable dual. Zippin’s theorem asserts that E embeds in a Banach space with a shrinking basis, and W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński have shown that E is a quotient of a Banach space with a shrinking basis. These two results use the interpolation theorem established by W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński. Here, we prove that the Szlenk indices of and can be controlled by the Szlenk index of E, where the Szlenk index...
(Annexe n° 1) Remarques sur l'exposé d'Assouad (n° XVI)
Approximation on Locally Convex Spaces.
Aspects of unconditionality of bases in spaces of compact operators
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 space...
is generated in strong operator topology by two of its elements
Banach S-algebras and conditional basic sequences in non-Montel Fréchet spaces
Banach spaces all of whose subspaces have the approximation property
Banach spaces and large cardinals
Banach spaces and operators which are nearly uniformly convex [Book]
Banach Spaces of Type p have Arbitrarily Distortable Subspaces.
Banach spaces quasi-reflexive of order one
Banach spaces with a supershrinking basis
We prove that a Banach space X with a supershrinking basis (a special type of shrinking basis) without copies is somewhat reflexive (every infinite-dimensional subspace contains an infinite-dimensional reflexive subspace). Furthermore, applying the -theorem by Rosenthal, it is proved that X contains order-one quasireflexive subspaces if X is not reflexive. Also, we obtain a characterization of the usual basis in .
Banach spaces with finite dimensional expansions of identity and universal bases of finite dimensional subspaces
Banach-Saks properties and spreading models.
Base d'ondelettes sur les groupes de Lie stratifiés