A Free Convenient Vector Space for Holomorphic Spaces.
A full characterization of multipliers for the strong -integral in the euclidean space
We study a generalization of the classical Henstock-Kurzweil integral, known as the strong -integral, introduced by Jarník and Kurzweil. Let be the space of all strongly -integrable functions on a multidimensional compact interval , equipped with the Alexiewicz norm . We show that each element in the dual space of can be represented as a strong -integral. Consequently, we prove that is strongly -integrable on for each strongly -integrable function if and only if is almost everywhere...
A General Approach to Infinite-Dimensional Holomorphy.
A generalization of an Ekeland-Lebourg theorem and the differentiability of distance functions
A Generalization Of Fubini's Theorem For Banach Algebra-Valued Measures.
A generalization of the interior mapping theorem of Clarke and Pourciau
A Generalization of the Strict Topology.
A generalized Pettis measurability criterion and integration of vector functions
For Banach-space-valued functions, the concepts of 𝒫-measurability, λ-measurability and m-measurability are defined, where 𝒫 is a δ-ring of subsets of a nonvoid set T, λ is a σ-subadditive submeasure on σ(𝒫) and m is an operator-valued measure on 𝒫. Various characterizations are given for 𝒫-measurable (resp. λ-measurable, m-measurable) vector functions on T. Using them and other auxiliary results proved here, the basic theorems of [6] are rigorously established.
A geometric characterization of the Radon-Nikodym property in Banach spaces
A Hahn-Banach extension theorem for analytic mappings
A Hahn-Banach Theorem for Holomorphic Mappings on Locally Convex Spaces.
A lifting theorem for locally convex subspaces of
We prove that for every closed locally convex subspace E of and for any continuous linear operator T from to there is a continuous linear operator S from to such that T = QS where Q is the quotient map from to .
A Lipschitz function which is on a.e. line need not be generically differentiable
We construct a Lipschitz function f on X = ℝ ² such that, for each 0 ≠ v ∈ X, the function f is smooth on a.e. line parallel to v and f is Gâteaux non-differentiable at all points of X except a first category set. Consequently, the same holds if X (with dimX > 1) is an arbitrary Banach space and “a.e.” has any usual “measure sense”. This example gives an answer to a natural question concerning the author’s recent study of linearly essentially smooth functions (which generalize essentially smooth...
A Measure Space Without the Strong Lifting Property.
A new proof of Fréchet differentiability of Lipschitz functions
We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on (or more generally on an Asplund space) has points of Fréchet differentiability. Somewhat more generally, we show that a real-valued Lipschitz function on a separable Banach space has points of Fréchet differentiability provided that the closure of the set of its points of Gâteaux differentiability is norm separable.
A new relationship between decomposability and convexity
In the present work we prove that, in the space of Pettis integrable functions, any subset that is decomposable and closed with respect to the topology induced by the so-called Alexiewicz norm (where ) is convex. As a consequence, any such family of Pettis integrable functions is also weakly closed.
A note on a class of Banach algebra-valued polynomials.
A note on a class of homeomorphisms between Banach spaces
This paper deals with homeomorphisms F: X → Y, between Banach spaces X and Y, which are of the form where is a continuous (2n+1)-linear operator.
A Note on a Support of a Linear Mapping
A Note on a Theorem of A. D. Alexandroff