A general topology approach to the study of differentiability of convex functions in Banach spaces
A generalization of an Ekeland-Lebourg theorem and the differentiability of distance functions
A generalization of reflexive Banach spaces and weakly compact operators
A generalized Kahane-Khinchin inequality
The inequality with an absolute constant C, and similar ones, are extended to the case of belonging to an arbitrary normed space X and an arbitrary compact group of unitary operators on X instead of the operators of multiplication by .
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.
A generalized -porous set with a small complement.
A geometric characterization of the Radon-Nikodym property in Banach spaces
A geometric form of the axiom of choice
A geometric version of the Moore theorem in the case of infinite dimensional Banach spaces.
A geometrical/combinatorical question with implications for the John-Nirenberg inequality for BMO functions
The first and last sections of this paper are intended for a general mathematical audience. In addition to some very brief remarks of a somewhat historical nature, we pose a rather simply formulated question in the realm of (discrete) geometry. This question has arisen in connection with a recently developed approach for studying various versions of the function space BMO. We describe that approach and the results that it gives. Special cases of one of our results give alternative proofs of the...
A Gowers tree like space and the space of its bounded linear operators
The famous Gowers tree space is the first example of a space not containing c₀, ℓ₁ or a reflexive subspace. We present a space with a similar construction and prove that it is hereditarily indecomposable (HI) and has ℓ₂ as a quotient space. Furthermore, we show that every bounded linear operator on it is of the form λI + W where W is a weakly compact (hence strictly singular) operator.
A Hahn-Banach extension theorem for analytic mappings
A Hahn-Banach Theorem in Conjugate Banach Spaces.
A Krein-Milman set without the integral representation property
A local characterization of Banach lattices with order continuous norm
A local metric characterization of Banach spaces
A lower bound on the radius of analyticity of a power series in a real Banach space
Let F be a power series centered at the origin in a real Banach space with radius of uniform convergence ϱ. We show that F is analytic in the open ball B of radius ϱ/√e, and furthermore, the Taylor series of F about any point a ∈ B converges uniformly within every closed ball centered at a contained in B.
A method for constructing orthonormal bases for non-archimedean Banach spaces of continuous functions
A method of reduction of constraints
A modification of Newton's method