is generated in strong operator topology by two of its elements
Baire classes of affine vector-valued functions
We investigate Baire classes of strongly affine mappings with values in Fréchet spaces. We show, in particular, that the validity of the vector-valued Mokobodzki result on affine functions of the first Baire class is related to the approximation property of the range space. We further extend several results known for scalar functions on Choquet simplices or on dual balls of L₁-preduals to the vector-valued case. This concerns, in particular, affine classes of strongly affine Baire mappings, the...
Baire classes of complex -preduals
Let be a complex -predual, non-separable in general. We investigate extendability of complex-valued bounded homogeneous Baire- functions on the set of the extreme points of the dual unit ball to the whole unit ball . As a corollary we show that, given , the intrinsic -th Baire class of can be identified with the space of bounded homogeneous Baire- functions on the set when satisfies certain topological assumptions. The paper is intended to be a complex counterpart to the same authors’...
Ball proximinality of closed * subalgebras in C(Q)
The notion of ball proximinality and the strong ball proximinality were recently introduced in [2]. We prove that a closed * subalgebra A of C(Q) is strongly ball proximinal in C(Q) and the metric projection from C(Q), onto the closed unit ball of A, is Hausdorff metric continuous and hence has continuous selection.
Ball proximinality of Equable spaces.
Ball remotal subspaces of Banach spaces
We study Banach spaces X with subspaces Y whose unit ball is densely remotal in X. We show that for several classes of Banach spaces, the unit ball of the space of compact operators is densely remotal in the space of bounded operators. We also show that for several classical Banach spaces, the unit ball is densely remotal in the duals of higher even order. We show that for a separable remotal set E ⊆ X, the set of Bochner integrable functions with values in E is a remotal set in L¹(μ,X).
Ball versus distance convexity of metric spaces.
Banach algebra techniques in the theory of arithmetic functions
For infinite discrete additive semigroups we study normed algebras of arithmetic functions endowed with the linear operations and the convolution. In particular, we investigate the problem of scaling the mean deviation of related multiplicative functions for . This involves an extension of Banach algebras of arithmetic functions by introducing weight functions and proving a weighted inversion theorem of Wiener type in the frame of Gelfand’s theory of commutative Banach algebras.
Banach lattices and infinite rigid sets.
Banach Lattices with Locally Compact Representation Spaces.
Banach S-algebras and conditional basic sequences in non-Montel Fréchet spaces
Banach spaces
Banach spaces, à la recherche du temps perdu.
What follows is the opening conference of the late night seminar at the III Conference on Banach Spaces held at Jarandilla de la Vera, Cáceres. Maybe the reader should not take everything what follows too seriously: after all, it was designed for a friendly seminar, late in the night, talking about things around a table shared by whisky, preprints and almonds. Maybe the reader should not completely discard it. Be as it may, it seems to me by now that everything arrives in the nick of time. A twisted...
Banach spaces all of whose subspaces have the approximation property
Banach spaces and bilipschitz maps
We show that a normed space E is a Banach space if and only if there is no bilipschitz map of E onto E ∖ {0}.
Banach spaces and large cardinals
Banach spaces and operators which are nearly uniformly convex [Book]
Banach Spaces Determined by Their Uniform Structures.
Banach spaces in which all multilinear forms are weakly sequentially continuous
We solve several problems in the theory of polynomials in Banach spaces. (i) There exist Banach spaces without the Dunford-Pettis property and without upper p-estimates in which all multilinear forms are weakly sequentially continuous: some Lorentz sequence spaces, their natural preduals and, most notably, the dual of Schreier's space. (ii) There exist Banach spaces X without the Dunford-Pettis property such that all multilinear forms on X and X* are weakly sequentially continuous; this gives an...
Banach spaces isomorphic to proper M-ideals