-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation.
(-)orthogonality in -adic Banach spaces
A Banach space that is MLUR but not HR.
A Banach space with a symmetric basis which contains no or , and all its symmetric basic sequences are equivalent
A bornological approach to rotundity and smoothness applied to approximation.
A characterization of -convexity and -convexity of Banach spaces.
A class of Banach sequence spaces analogous to the space of Popov
Hagler and the first named author introduced a class of hereditarily Banach spaces which do not possess the Schur property. Then the first author extended these spaces to a class of hereditarily Banach spaces for . Here we use these spaces to introduce a new class of hereditarily Banach spaces analogous of the space of Popov. In particular, for the spaces are further examples of hereditarily Banach spaces failing the Schur property.
A coding of separable Banach spaces. Analytic and coanalytic families of Banach spaces
When the set of closed subspaces of C(Δ), where Δ is the Cantor set, is equipped with the standard Effros-Borel structure, the graph of the basic relations between Banach spaces (isomorphism, being isomorphic to a subspace, quotient, direct sum,...) is analytic non-Borel. Many natural families of Banach spaces (such as reflexive spaces, spaces not containing ℓ₁(ω),...) are coanalytic non-Borel. Some natural ranks (rank of embedding, Szlenk indices) are shown to be coanalytic ranks. Applications...
A coefficient related to some geometric properties of a Banach space.
A common fixed point theorem for a commuting family of weak* continuous nonexpansive mappings
It is shown that if 𝓢 is a commuting family of weak* continuous nonexpansive mappings acting on a weak* compact convex subset C of the dual Banach space E, then the set of common fixed points of 𝓢 is a nonempty nonexpansive retract of C. This partially solves an open problem in metric fixed point theory in the case of commutative semigroups.
A comparative analysis of Bernstein type estimates for the derivative of multivariate polynomials
We compare the yields of two methods to obtain Bernstein type pointwise estimates for the derivative of a multivariate polynomial in a domain where the polynomial is assumed to have sup norm at most 1. One method, due to Sarantopoulos, relies on inscribing ellipses in a convex domain K. The other, pluripotential-theoretic approach, mainly due to Baran, works for even more general sets, and uses the pluricomplex Green function (the Zaharjuta-Siciak extremal function). When the inscribed ellipse method...
A conjecture about the Dunford-Pettis property
A continuous surjection from the unit interval onto the unit square.
A continuum of totally incomparable hereditarily indecomposable Banach spaces
A family is constructed of cardinality equal to the continuum, whose members are totally incomparable hereditarily indecomposable Banach spaces.
A contractive fixed point free mapping on a weakly compact convex set
We prove the existence of a contractive mapping on a weakly compact convex set in a Banach space that is fixed point free. This answers a long-standing open question.
A contribution to a theorem of Ulam and Mazur.
A curious generalization of local uniform rotundity
A dichotomy on Schreier sets
We show that the Schreier sets have the following dichotomy property. For every hereditary collection ℱ of finite subsets of ℱ, either there exists infinite such that , or there exist infinite such that .
A generalization of an Ekeland-Lebourg theorem and the differentiability of distance functions
A generalized projection decomposition in Orlicz-Bochner spaces
In this paper, a precise projection decomposition in reflexive, smooth and strictly convex Orlicz-Bochner spaces is given by the representation of the duality mapping. As an application, a representation of the metric projection operator on a closed hyperplane is presented.