Related papers: Projection constants for spaces of multivariate po…

In the present paper we investigate some geometrical properties of the norms in Banach function spaces. Particularly there is shown that if exponent $1/p(\cdot)$ belongs to $BLO^{1/\log}$ then for the norm of corresponding variable exponent…

We prove that weakly unconditionally Cauchy (w.u.C.) series and unconditionally converging (u.c.) series are preserved under the action of polynomials or holomorphic functions on Banach spaces, with natural restrictions in the latter case.…

We find large classes of injective and projective $p$-multinormed spaces. In fact, these classes are universal, in the sense that every $p$-multinormed space embeds into (is a quotient of) an injective (resp. projective) $p$-multinormed…

According to a result due to B.T. Polyak, a mapping between Hilbert spaces, which is $C^{1,1}$ around a regular point, carries a ball centered at that point to a convex set, provided that the radius of the ball is small enough. The present…

We define a notion of global analytic space with overconvergent structure sheaf. This gives an analog on a general base Banach ring of Grosse-Kloenne's overconvergent p-adic spaces and of Bambozzi's generalized affinoid varieties over R.…

We define the $k$:th moment of a Banach space valued random variable as the expectation of its $k$:th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. We study both the projective…

Poincar\'{e}-Sobolev-type inequalities involving rearrangement-invariant norms on the entire $\mathbb{R}^n$ are provided. Namely, inequalities of the type $\|u-P\|_{Y(\mathbb{R}^n)}\leq C\|\nabla^m u\|_{X(\mathbb{R}^n)}$, where $X$ and $Y$…

In this paper we discuss symmetrically self-dual spaces, which are simply real vector spaces with a symmetric bilinear form. Certain subsets of the space will be called q-positive, where q is the quadratic form induced by the original…

For various Hilbert spaces of analytic functions on the unit disk, we characterize when a function $f$ has optimal polynomial approximants given by truncations of a single power series. We also introduce a generalized notion of optimal…

This article delves into an exploration of two innovative constants, namely DW(X,{\alpha},\b{eta}) and DWB (X,{\alpha},\b{eta}), both of which constitute extensions of the Dunkl-Williams constant. We derive both the upper and lower bounds…

We investigate the conditional distributions of two Banach space valued, jointly Gaussian random variables. In particular, we show that these conditional distributions are again Gaussian and that their means and covariances can be…

Let $E$ and $G$ be two Banach function spaces, let $T \in \mathcal{L}(E,Y)$, and let ${\langle X,Y \rangle}$ be a Banach dual pair. In this paper we give conditions for which there exists a (necessarily unique) bounded linear operator…

Recently, samplets have been introduced as localized discrete signed measures which are tailored to an underlying data set. Samplets exhibit vanishing moments, i.e., their measure integrals vanish for all polynomials up to a certain degree,…

Let $(M,\rho)$ be a metric space and let $Y$ be a Banach space. Given a positive integer $m$, let $F$ be a set-valued mapping from $M$ into the family of all compact convex subsets of $Y$ of dimension at most $m$. In this paper we prove a…

Let (e^{tA})_{t \geq 0} be a C_0-contraction semigroup on a 2-smooth Banach space E, let (W_t)_{t \geq 0} be a cylindrical Brownian motion in a Hilbert space H, and let (g_t)_{t \geq 0} be a progressively measurable process with values in…

The notions of $p$-convexity and concavity are fundamental tools for studying Banach lattices, as they partition the class of Banach lattices into a scale of spaces with $L_p$-like properties. Upper and lower $p$-estimates provide a…

A Banach space valued graphon is a function $W:(\Omega, \mathcal{A},\pi)^2\to\mathcal{Z}$ from a probability space to a Banach space with a separable predual, measurable in a suitable sense, and lying in appropriate $L^p$-spaces. As such we…

In this paper, we introduce the concept of isotone cones in Banach spaces. Then we apply the order monotonic property of the metric projection operator to prove the existence of best approximations for some operators without continuity…

We consider ordered pairs $(X,\mathcal{B})$ where $X$ is a finite set of size $v$ and $\mathcal{B}$ is some collection of $k$-element subsets of $X$ such that every $t$-element subset of $X$ is contained in exactly $\lambda$ "blocks" $B\in…

Let $(\varphi_t)_{t\geq 0} $ a semigroup of holomorphic self-maps of the unit disk and $C_t f = f \circ \varphi_t $ the semigroup of composition operators which corresponds to $\varphi_t. $ Given a non-separable Banach space of analytic…