Related papers: Anisotropic spaces for the bilateral shift
A Banach space contains asymptotically isometric copies of $\ell_1$ if and only if its dual space contains an isometric copy of $L_1$.
We construct a Banach manifold of states, which are Gibbs states for potentials that are form-bounded in the sense of Kato relative to the free Hamiltonian. We construct the (+1)-affine structure and the (+1)-affine connection in the sense…
We construct generalised shift-invariant systems of functions of several real variables for anisotropic Besov spaces that can be generated by the decomposition method using any given expansive matrix and establish the conditions on those…
A dual Banach algebra is a Banach algebra which is a dual space, with the multiplication being separately weak$^*$-continuous. We show that given a unital dual Banach algebra $\mc A$, we can find a reflexive Banach space $E$, and an…
The Abelian Higgs model with anisotropic couplings in 2+1 dimensions is studied in both the compact and non-compact formulations. Decoupling of the space-like planes takes place in the extreme anisotropic limit, so charged particles and…
Given a two-sided shift space on a finite alphabet and a continuous potential function, we give conditions under which an equilibrium measure can be described using a construction analogous to Hausdorff measure that goes back to the work of…
It is introduced an open class of linear operators on Banach and Hilbert spaces such that their non-wandering set is an infinite dimensional topologically mixing subspace. In certain cases, the non-wandering set coincides with the whole…
In this paper structure of infinite dimensional Banach spaces is studied by using an asymptotic approach based on stabilization at infinity of finite dimensional subspaces which appear everywhere far away. This leads to notions of…
We theoretically investigate the control of the Goos-H\"anchen shift (GHS) of a reflected weak probe field in both parity-time ($\mathcal{PT}$)-symmetric and conventional optomechanical systems. The proposed scheme consists of a single…
The Lipschitz space of an infinite (locally-finite) graph is defined as the set of functions on the vertices of the graph such that the differences of the values between adjacent vertices remain bounded. In this paper we prove that this set…
We consider similarity transformations of a perturbed linear operator $A-B$ in a complex Banach space $\mathcal{X}$, where the unperturbed operator $A$ is a generator of a Banach $L_1(\mathbb{R})$-module and the perturbation operator $B$ is…
The scalar field exchange diagram for the correlation function of four scalar operators is evaluated in anti-de Sitter space, $AdS_{d+1}$. The conformal dimensions $\Delta_i$, $i=1,...,4$ of the scalar operators and the dimension $\Delta$…
We extend a number of results from one dimensional dynamics based on spectral properties of the Ruelle-Perron-Frobenius transfer operator to Anosov diffeomorphisms on compact manifolds. This allows to develop a direct operator approach to…
We report the discovery of two new invariants for three-qubit states which, similarly to the 3-tangle, are invariant under local unitary transformations and permutations of the parties. These quantities have a direct interpretation in terms…
We present a sufficient condition for a Banach space to have the approximate hyperplane series property (AHSP) which actually covers all known examples. We use this property to get a stability result to vector-valued spaces of integrable…
In this paper, we study {\it operator spaces\/} in the sense of the theory developed recently by Blecher-Paulsen [BP] and Effros-Ruan [ER1]. By an operator space, we mean a closed subspace $E\subset B(H)$, with $H$ Hilbert. We will be…
The purpose of this note is to show that, if $\mcB$ is a uniformly convex Banach, then the dual space $\mcB'$ has a "Hilbert space representation" (defined in the paper), that makes $\mcB$ much closer to a Hilbert space then previously…
We construct a Hereditarily Indecomposable Banach space $\eqs_d$ with a Schauder basis \seq{e}{n} on which there exist strictly singular non-compact diagonal operators. Moreover, the space $\mc{L}_{\diag}(\eqs_d)$ of diagonal operators with…
The convex-transitivity property can be seen as a convex generalization of the almost transitive (or quasi-isotropic) group action of the isometry group of a Banach space on its unit sphere. We will show that certain Banach algebras,…
In this paper we study subspaces which are invariant under squares and cubes (separately as well as jointly) of unicellular backward weighted shift operators on a separable Hilbert space. The finite-dimensional subspaces are characterized…