Related papers: Bochner integrals in ordered vector spaces

In this work, we construct and study certain classes of infinite dimensional Lie groups that are modelled on weighted function spaces. In particular, we construct a Lie group of weighted diffeomorphisms on a Banach space. Further, we also…

Given $\u$ a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type, $H_{b\u}(E)$. We prove that, under very natural conditions verified by many usual classes of…

A positive operator $T:E\to E$ on a Banach lattice $E$ with an order continuous norm is said to be $\mathfrak{B}$-Volterra with respect to a Boolean algebra $\mathfrak{B}$ of order projections of $E$ if the bands canonically corresponding…

This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and…

A function on the real line is called regulated if it has a left limit and a right limit at each point. If $f$ is a Schwartz distribution on the real line such that $f=F'$ (distributional or weak derivative) for a regulated function $F$…

Given a compact space $X$ and a commutative Banach algebra $A$, the character spaces of $A$-valued function algebras on $X$ are investigated. The class of natural $A$-valued function algebras, those whose characters can be described by…

Given a linear closed but not necessarily densely defined operator $A$ on a Banach space $E$ with nonempty resolvent set and a multivalued map $F\colon I\times E\map E$ with weakly sequentially closed graph, we consider the…

It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm which is itself locally uniformly convex. It follows that on any such space all continuous real-valued functions may be uniformly approximated by…

We study Henstock-type integrals for functions defined in a compact metric space $T$ endowed with a regular $\sigma$-additive measure $\mu$, and taking values in a Banach lattice $X$. In particular, the space $[0,1]$ with the usual Lebesgue…

In this paper, we present some implicit function theorems for set-valued mappings between Fr\'echet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence…

In this work cylindrical Wiener processes on Banach spaces are defined by means of cylindrical stochastic processes, which are a well considered mathematical object. This approach allows a definition which is a simple straightforward…

A classical technique to construct polynomial preserving extensions of scalar functions defined on the boundary of an $n$ simplex to the interior is to use so-called rational blending functions. The purpose of this paper is to generalize…

We study some aspects of countably additive vector measures with values in $\ell_\infty$ and the Banach lattices of real-valued functions that are integrable with respect to such a vector measure. On the one hand, we prove that if $W…

We work with very general Banach spaces of analytic functions in the disk or other domains which satisfy a minimum number of natural axioms. Among the preliminary results, we discuss some implications of the basic axioms and identify all…

Let B(X) be the algebra of all bounded linear operators on a complex Banach space X with dim X greater than 3. In this paper, we characterize the forms of surjective linear maps on B(X) which preserve the dimension of the vector space…

Let $E$ be a separable Banach space and $\Omega$ be a compact Hausdorff space. It is shown that the space $C(\Omega,E)$ has property (V) if and only if $E$ does. Similar result is also given for Bochner spaces $L^p(\mu,E)$ if $1<p<\infty$…

Recently we have presented a unified approach to two classes of Banach spaces defined by means of variations (Waterman spaces and Chanturia classes), utilizing the concepts from the theory of ideals on the set of natural numbers. We defined…

After calculating the Dushnik-Miller dimension of Minkowski spaces to be countable infinity, we define a novel notion of dimension for ordered spaces recovering the correct manifold dimension and obtain a corresponding obstruction for the…

We construct Zachary space in $\R^\infty$ and find that this is a Banach space of functions of bounded mean oscillation with order $p, 1\leq p \leq \infty$ containing the function of bounded mean oscillation $BMO[\R_I^\infty]$ as a dense…

Butcher series, also called B-series, are a type of expansion, fundamental in the analysis of numerical integration. Numerical methods that can be expanded in B-series are defined in all dimensions, so they correspond to \emph{sequences of…