Obstacles to bounded recovery.
On a direct decomposition of the space .
On a semigroup of modular functions with involution.
On Banach Spaces with the Gelfand-Philips Property.
On Banach spaces X such that L(Lp,X) = K(Lp,X).
On bases, compactness and weak convergence in the Banach space
On basic Hahn-Banach extensions
On Compactness in L...(..., X) in the Weak Topology and in the Topology ...(L...(..., X), L...(..., X')).
On complemented copies of in spaces of operators, II
We show that as soon as embeds complementably into the space of all weakly compact operators from to , then it must live either in or in .
On complemented copies of c₀(ω₁) in C(Kⁿ) spaces
Given a compact Hausdorff space K we consider the Banach space of real continuous functions C(Kⁿ) or equivalently the n-fold injective tensor product or the Banach space of vector valued continuous functions C(K,C(K,C(K...,C(K)...). We address the question of the existence of complemented copies of c₀(ω₁) in under the hypothesis that C(K) contains such a copy. This is related to the results of E. Saab and P. Saab that contains a complemented copy of c₀ if one of the infinite-dimensional Banach...
On complemented subspaces of rearrangement invariant function spaces.
A necessary and sufficient condition is given for a rearrangement invariant function space to contain a complemented isomorphic copy of l1(l2).
On copies of in the bounded linear operator space
In this note we study some properties concerning certain copies of the classic Banach space in the Banach space of all bounded linear operators between a normed space and a Banach space equipped with the norm of the uniform convergence of operators.
On copies of c0 in some function spaces.
On decompositions of Banach spaces into a sum of operator ranges
It is proved that a separable Banach space X admits a representation as a sum (not necessarily direct) of two infinite-codimensional closed subspaces and if and only if it admits a representation as a sum (not necessarily direct) of two infinite-codimensional operator ranges. Suppose that a separable Banach space X admits a representation as above. Then it admits a representation such that neither of the operator ranges , contains an infinite-dimensional closed subspace if and only...
On embedding l1 as a complemented subspace of Orlicz vector valued function spaces.
Several conditions are given under which l1 embeds as a complemented subspace of a Banach space E if it embeds as a complemented subspace of an Orlicz space of E-valued functions. Previous results in Pisier (1978) and Bombal (1987) are extended in this way.
On embeddings of C₀(K) spaces into C₀(L,X) spaces
For a locally compact Hausdorff space K and a Banach space X let C₀(K, X) denote the space of all continuous functions f:K → X which vanish at infinity, equipped with the supremum norm. If X is the scalar field, we denote C₀(K, X) simply by C₀(K). We prove that for locally compact Hausdorff spaces K and L and for a Banach space X containing no copy of c₀, if there is an isomorphic embedding of C₀(K) into C₀(L,X), then either K is finite or |K| ≤ |L|. As a consequence, if there is an isomorphic embedding...
On essentially incomparable Banach spaces.
On inclusion relations between Lorentz sequence spaces and inequalities of Lewis type.
On Incomparability of Banach Spaces.
On incomparability of Banach spaces.