The class of countably intersected families of sets is defined. For any such family we define a Banach space not containing l(N). Thus we obtain counterexamples to certain questions related to the heredity problem for W.C.G. Banach spaces. Among them we give a subspace of a W.C.G. Banach space not containing l(N) and not being itself a W.C.G. space. INTRODUCTION In the present paper we deal wit...

Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X, ‖ · ‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = R this construction yields a norm such that D(R) becomes a Banach space. Furthermore, we show that for a real Banach space...

If X is a Banach space such that the isomorphism constant to `2 from n dimensional subspaces grows sufficiently slowly as n → ∞, then X has the approximation property. A consequence of this is that there is a Banach space X with a symmetric basis but not isomorphic to `2 so that all subspaces of X have the approximation property. This answers a problem raised in 1980 [8]. An application of the ...

in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...

Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.

It is proved that there exist complemented subspaces of countable topo-logical products (locally convex direct sums) of Banach spaces which cannot be represented as topological products (locally convex direct sums) of Banach spaces The problem of description of complemented subspaces of a given locally convex space is one of the general problems of structure theory of locally convex spaces. In ...

We introduce property (FS), which asserts that a Banach space has many c0-\sub-decompositions", and show that if X is a Banach space with property (FS) and X is isomorphic tò1, then X itself is isomorphic to c0.

It is proved that if a Banach space Y is a quotient of a Banach space having a shrinking unconditional basis, then every normalized weakly null sequence in Y has an unconditional subsequence. The proof yields the corollary that every quotient of Schreier's space is c o-saturated. §0. Introduction. We shall say that a Banach space Y has property (WU) if every normalized weakly null sequence in Y...

The Banach frame for a Banach space  can reconstruct each vector in  by the pre-frame operator or the reconstruction operator. The Banach Λ-frame for operator spaces was introduced by Kaushik, Vashisht and Khattar [Reconstruction Property and Frames in Banach Spaces, Palestine Journal of Mathematics, 3(1), 2014, 11-26]. In this paper we give necessary and sufficient conditions for the existen...

We study certain Banach spaces that are added in the extension by one Cohen real. Specifically, we show that adding just one Cohen real to any model adds a Banach space of density א1 which does not embed into any such space in the ground model (Theorem 1.1). Moreover, such a Banach space can be chosen to be UG (Theorem 1.6). This has consequences on the the isomorphic universality number for Ba...