Related papers: Anisotropic spaces for the bilateral shift

Denote the points in {1,2,..,r}^{Z}= {1,2,..,r}^{N} x {1,2,..,r}^{N} by ({y}^*, {x}). Given a Lipschitz continuous observable A: {1,2,..,r}^{Z} \to {R} , we define the map {G}^+: {H}\to {H} by {G}^+(\phi)({y}^*) = \sup_{\mu \in {M}_\sigma}…

In this paper, two related types of dualities are investigated. The first is the duality between left-invertible operators and the second is the duality between Banach spaces of vector-valued analytic functions. We will examine a pair…

A class of maps in a complex Banach space is studied, which includes both unbounded linear operators and nonlinear holomorphic maps. The defining property, which we call {\sl pseudo-contractivity}, is introduced by means of the Abel…

Let $f:X\to X$ be an invertible Lipschitz transformation on a compact metric space $X$. Given a H\"{o}lder continuous invertible operator cocycles on a Banach space and an $f$-invariant ergodic measure, this paper establishes the H\"{o}lder…

We provide sufficient conditions for a mapping between two Banach spaces to be a diffeomorphism using the approach of an auxiliary functional and also by the aid of a duality mapping corresponding to a normalization function. We simplify…

We characterize weak* closed unital vector spaces of operators on a Hilbert space $H$. More precisely, we first show that an operator system, which is the dual of an operator space, can be represented completely isometrically and weak*…

Classes of Banach spaces that are finitely, strongly finitely or elementary equivalent are introduced. On sets of these classes topologies are defined in such a way that sets of defined classes become compact totally disconnected…

We study the asymptotic behavior of almost-orbits of abstract evolution systems in Banach spaces with or without a Lipschitz assumption. In particular, we establish convergence, convergence in average and almost-convergence of almost-orbits…

We show that for a very wide class of Banach spaces of functions on [0,1] there are intrinsic lower bounds for the essential spectral radius of the transfer operator associated to piecewise smooth expanding maps. The class of Banach spaces…

In the paper is considered two problems on extension of operators whose range space for the first problem (or domain space for the second one) belongs to the fixed class of finite equivalence, which is generated by a given Banach space $X$.…

For any $C^r$ contact Anosov flow with $r\ge 3$, we construct a scale of Hilbert spaces, which are embedded in the space of distributions on the phase space and contain all $C^r$ functions, such that the transfer operators for the flow…

We prove bilinear inequalities for differential operators in $\mathbb{R}^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However,…

We improve the known results about the complexity of the relation of isomorphism between separable Banach spaces up to Borel reducibility, and we achieve this using the classical spaces $c_0$, $\ell_p$ and $L_p$, $1 \leq p <2$. More…

We characterize real Banach spaces $Y$ such that the pair $(\ell_\infty ^n, Y)$ has the Bishop-Phelps-Bollob\'as property for operators. To this purpose it is essential the use of an appropriate basis of the domain space $\R^n$. As a…

Let $p(\cdot):\ {\mathbb{R}^n}\to(0,\infty)$ be a variable exponent function satisfying the globally log-H\"{o}lder continuous condition and $A$ a general expansive matrix on ${\mathbb{R}^n}$. In this article, the authors introduce the…

We consider a matter wave packet of cold atom gas impinging upon a step potential created by the optical light field. In the presence of spin-orbit (SO) coupling, the atomic eigenstates contain two types of evanescent states, one of which…

Density function theory is the workhorse of modern electronic structure theory. However, its accuracy in practical calculations is limited by the choice of the exchange-correlation potential. In this respect, two-dimensional materials pose…

Suppose $E$ is fully symmetric Banach function space on $(0,1)$ or $(0,\infty)$ or a fully symmetric Banach sequence space. We give necessary and sufficient conditions on $f\in E$ so that its orbit $\Omega(f)$ is the closed convex hull of…

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…

It is a longstanding problem whether every contractible Banach algebra is necessarily finite-dimensional. In this note, we confirm this for Banach algebras acting on Banach spaces with the uniform approximation property. This generalizes a…