Related papers: An alternative approach to weighted non-commutativ…
The dynamics of weighted translation operators on Lebesgue spaces, Orlicz spaces, and in general on solid Banach function spaces have been studied in numerous papers. Recently, the dynamics of weighted translations on weighted Orlicz spaces…
We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…
We construct a countable inductive limit of weighted Banach spaces of holomorphic functions, which is not a topological subspace of the corresponding weighted inductive limit of spaces of continuous functions. The main step of our…
We introduce new weighted $L^p$-type spaces defined in terms of weight function matrices and characterize the inclusion relations in terms of the defining matrices. Moreover, we provide a detailed study concerning the coincidence with the…
Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such…
We characterize all entire functions that transform a weighted Banach spaces of analytic functions $\mathcal{H}^{\infty}_{\mu_1}$ into another space of the same kind $\mathcal{H}^{\infty}_{\mu_2}$ by superposition for very general weights…
Geodesic contraction in vector-valued differential equations is readily verified by linearized operators which are uniformly negative-definite in the Riemannian metric. In the infinite-dimensional setting, however, such analysis is…
This article introduces an innovative mathematical framework designed to tackle non-linear convex variational problems in reflexive Banach spaces. Our approach employs a versatile technique that can handle a broad range of variational…
In this paper we consider the properties of sums of rearrangement-invariant quasi-Banach function spaces, with the focus being on rearrangement-invariance and the Fatou property. In our first main result, we show that the quasinorm of the…
Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in $\bf R$.…
We define a new rearrangement, called rearrangement by tamping, for non-negative measurable functions defined on R+. This rearrangement has many properties in common with the well-known Schwarz non-increasing rearrangement such as the…
We introduce a family of Banach spaces of measures, each containing the set of measures with density of bounded variation. These spaces are suitable for the study of weighted transfer operators of piecewise-smooth maps of the interval where…
We construct continuous (and even invertible) linear operators acting on Banach (even Hilbert) spaces whose restrictions to their respective closed linear subspaces of chain recurrent vectors are not chain recurrent operators. This…
We present in this paper a new way to define weighted Sobolev spaces when the weight functions are arbitrary small. This new approach can replace the old one consisting in modifying the domain by removing the set of points where at least…
In this paper we recontextualize the theory of matrix weights within the setting of Banach lattices. We define an intrinsic notion of directional Banach function spaces, generalizing matrix weighted Lebesgue spaces. Moreover, we prove an…
Let $\cal M$ be a semi-finite von Neumann algebra equipped with a distinguished faithful, normal, semi-finite trace $\tau$. We introduce the notion of equi-integrability in non-commutative spaces and show that if a rearrangement invariant…
The purpose of this paper is devoted to studying representation of measures of non generalized compactness, in particular, measures of noncompactness, of non-weak compactness, and of non-super weak compactness, etc, defined on Banach spaces…
In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results.…
We introduce a modified version of the Whitney extension operators for collections of functions from a closed subset of $\mathbb{R}^n$ into scales of Banach spaces with smoothing operators. We prove an extension theorem for collections…
We describe the spectrum of weighted $d$-isomorphisms of Banach lattices restricted on closed subspaces that are "rich" enough to preserve some "memory" of the order structure of the original lattice. The examples include (but are not…