Banach spaces which are -ideals in their bidual have property
We show that every Banach space which is an -ideal in its bidual has the property of Pelczynski. Several consequences are mentioned.
Banach spaces which are proper M-ideals
Banach spaces which are semi-L-summands in their biduals.
Banach spaces which embed into their dual
We use Birkhoff-James' orthogonality in Banach spaces to provide new conditions for the converse of the classical Riesz representation theorem.
Banach spaces whose bounded sets are bounding in the bidual.
Banach spaces widely complemented in each other
Suppose that X and Y are Banach spaces that embed complementably into each other. Are X and Y necessarily isomorphic? In this generality, the answer is no, as proved by W. T. Gowers in 1996. However, if X contains a complemented copy of its square X², then X is isomorphic to Y whenever there exists p ∈ ℕ such that can be decomposed into a direct sum of and Y. Motivated by this fact, we introduce the concept of (p,q,r) widely complemented subspaces in Banach spaces, where p,q and r ∈ ℕ. Then,...
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 spaces with small Calkin algebras
Let X be a Banach space. Let 𝓐(X) be a closed ideal in the algebra ℒ(X) of the operators acting on X. We say that ℒ(X)/𝓐(X) is a Calkin algebra whenever the Fredholm operators on X coincide with the operators whose class in ℒ(X)/𝓐(X) is invertible. Among other examples, we have the cases in which 𝓐(X) is the ideal of compact, strictly singular, strictly cosingular and inessential operators, and some other ideals introduced as perturbation classes in Fredholm theory. Our aim is to present some...
Banach Spaces with the Condition of Mazur.
Banach spaces with the differentiable norms
Banach spaces without minimal subspaces – Examples
We analyse several examples of separable Banach spaces, some of them new, and relate them to several dichotomies obtained in [11],by classifying them according to which side of the dichotomies they fall.
Banach triples with generalized inverses.
Banach-Euclidean four-point properties
Banachian Differentiable Spaces.
Banach-Mackey, locally complete spaces, and -summability.
Banach-Mackey spaces.
Banach-Mazur distance of central sections of a centrally symmetric convex body.
Banach-Mazur Distances and Projections on p-convex Spaces.
Banach-power-associative algebras and J-B algebras