Products and factors of Banach function spaces [PDF]
Given two Banach function spaces we study the pointwise product space E.F, especially for the case that the pointwise product of their unit balls is again convex. We then give conditions on when the pointwise product E . M(E, F)=F, where M(E,F) denotes the space of multiplication operators from E into F.
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A proof of Esterle's conjecture on negative powers of Hilbert‐space contractions
Abstract We establish the following result, confirming a conjecture of Jean Esterle. For each closed subset E$E$ of the unit circle of Lebesgue measure zero, there exists a positive sequence un→∞$u_n\rightarrow \infty$ with the following property: If T$T$ is a contraction on a Hilbert space such that σ(T)⊂E$\sigma (T)\subset E$ and ∥T−n∥=O(un)$\Vert T^{
Thomas Ransford
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Double-dual n-types over Banach spaces not containing ℓ1
Let E be a Banach space. The concept of n-type overE is introduced here, generalizing the concept of type overE introduced by Krivine and Maurey. Let E″ be the second dual of E and fix g″1,…g″n∈E″.
Markus Pomper
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Metric spaces with small rough angles and the rectifiability of rough self‐contracted curves
Abstract The small rough angle (SRA$\operatorname{SRA}$) condition, introduced by Zolotov in arXiv:1804.00234, captures the idea that all angles formed by triples of points in a metric space are small. In the first part of the paper, we develop the theory of metric spaces (X,d)$(X,d)$ satisfying the SRA(α)$\operatorname{SRA}(\alpha)$ condition for some
Estibalitz Durand Cartagena +1 more
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Equidistribution in 2‐nilpotent Polish groups and triple restricted sumsets
Abstract The aim of this paper is to establish a Ratner‐type equidistribution theorem for orbits on homogeneous spaces associated with 2$\hskip.001pt 2$‐nilpotent locally compact Polish groups under the action of a countable discrete abelian group.
Ethan Ackelsberg, Asgar Jamneshan
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Banach Spaces and Algebras of Continuous Functions [PDF]
this space becomes a real Banach space. Finally, provided with the usual multiplication of functions, this space becomes a real Banach algebra. The function which is identically one on X is the multiplicative identity, and we denote it by e. According to the Banach-Stone theorem [5],2 if X is compact, then the topology of X is reflected in the ...
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A Theorem of Rolewicz's Type for Measurable Evolution Families in Banach Spaces [PDF]
Let $varphi$ be a positive and non-decreasing function defined on the real half-line and ${mathcal U}$ be a strongly measurable, exponentially bounded evolution family of bounded linear operators acting on a Banach space and satisfing a certain ...
Constantin Buse +3 more
core
A new approach for the analysis of evolution partial differential equations on a finite interval
Abstract We show that, for certain evolution partial differential equations, the solution on a finite interval (0,ℓ)$(0,\ell)$ can be reconstructed as a superposition of restrictions to (0,ℓ)$(0,\ell)$ of solutions to two associated partial differential equations posed on the half‐lines (0,∞)$(0,\infty)$ and (−∞,ℓ)$(-\infty,\ell)$.
Türker Özsarı +2 more
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Well‐posedness of heat equations with nonlinearities of arbitrarily rapid growth
Abstract We address local‐ and global‐in‐time well‐posedness of the Cauchy problem for nonlinear heat equations without imposing growth rate restrictions on the nonlinearity a priori. Our results constitute a nontrivial expansion of the classical Lq$L^q$‐theory for nonlinearities dominated by polynomial growth and the exponential‐Orlicz space theory ...
Yohei Fujishima +2 more
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On Solutions of the Nonlocal Generalized Coupled Langevin-Type Pantograph Systems
This paper concentrates on the analysis of a category of coupled Langevin-type pantograph differential equations involving the generalized Caputo fractional derivative with nonlocal conditions.
Houari Bouzid +4 more
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