Related papers: The polarization constant of finite dimensional co…

A Banach space $X$ has the ball fixed point property (BFPP) if for every closed ball $B$ and for every nonexpansive mapping $T\colon B\to B$, there is a fixed point. We study the BFPP for $C(K)$-spaces. Our goal is to determine topological…

Given any Banach space $X$, let $L_2^X$ denote the Banach space of all measurable functions $f:[0,1]\to X$ for which ||f||_2:=(int_0^1 ||f(t)||^2 dt)^{1/2} is finite. We show that $X$ is a UMD--space (see \cite{BUR:1986}) if and only if…

We develop a nonperturbative approach to the bulk polarization of crystalline electric insulators in $d\geq1$ dimensions. Formally, we define polarization via the response to background fluxes of both charge and lattice translation…

We find an optimal upper bound on the values of the weak$^*$-dentability index $Dz(X)$ in terms of the Szlenk index $Sz(X)$ of a Banach space $X$ with separable dual. Namely, if $\;Sz(X)=\omega^{\alpha}$, for some $\alpha<\omega_1$, and…

Given any square matrix or a bounded operator $A$ in a Hilbert space such that $p(A)$ is normal (or similar to normal), we construct a Banach algebra, depending on the polynomial $p$, for which a simple functional calculus holds. When the…

We show that norms on certain Banach spaces $X$ can be approximated uniformly, and with arbitrary precision, on bounded subsets of $X$ by $C^{\infty}$ smooth norms and polyhedral norms. In particular, we show that this holds for any…

The Cluster Value Theorem is known for being a weak version of the classical Corona Theorem. Given a Banach space $X$, we study the Cluster Value Problem for the ball algebra $A_u(B_X)$, the Banach algebra of all uniformly continuous…

For each sequence X of finite-dimensional Banach spaces there exists a sequence H of finite connected nweighted graphs with maximum degree 3 such that the following conditions on a Banach space Y are equivalent: (1) Y admits uniformly…

We introduced the concept of strong property $(\mathbb{B})$ with a constant for Banach algebras and, by applying certain analysis on the Fourier algebra of a unit circle, we show that all C$^*$-algebras and group algebras have the strong…

In this paper, we use the Mordukhovich derivatives to precisely find the covering constants for the metric projection operator onto nonempty closed and convex subsets in uniformly convex and uniformly smooth Banach spaces. We consider three…

It is consistent with any possible value of the continuum $\mathfrak{c}$ that every infinite-dimensional Banach space of density $\leq \mathfrak{c}$ condenses onto the Hilbert cube. Let $\mu$ be a cardinal of uncountable cofinality. It is…

Linearly polarized emission is described, in general, in terms of the Stokes parameters $Q$ and $U$, from which the polarization intensity and polarization angle can be determined. Although the polarization intensity and polarization angle…

It is shown that if (X,||.||_X) is a Banach space with Rademacher type p \ge 1, then for every integer n there exists an even integer m < Cn^{2-1/p}log n (C is an absolute constant), such that for every f:Z_m^n --> X, \Avg_{x,\e}[||f(x+…

We consider a three dimensional Wigner crystal of electrons lying in a host ionic dielectric. Owing to their interaction with the lattice polarization, each localized electron forms a polaron. We study the collective excitations of such a…

A continuous complex-valued function $F$ in a domain $D\subseteq\mathbf{C}$ is Poly-analytic of order $\alpha$ if it satisfies $\partial^{\alpha}_{\overline{z}}F=0.$ One can show that $F$ has the form…

We consider abstract inverse problems between infinite-dimensional Banach spaces. These inverse problems are typically nonlinear and ill-posed, making the inversion with limited and noisy measurements a delicate process. In this work, we…

We study the group invariant continuous polynomials on a Banach space $X$ that separate a given set $K$ in $X$ and a point $z$ outside $K$. We show that if $X$ is a real Banach space, $G$ is a compact group of $\mathcal{L} (X)$, $K$ is a…

Particles scattered off the nuclear target acquire a polarization if the nuclei have a non zero analyzing power. This effect is enhanced when particles traverse a bent crystal. Such enhancement under certain assumptions allows one to…

The notion of polarity between sets, well-known from convex geometry, is a geometric version of the Fourier transform. We exploit this analogy to propose a new simple definition of quantum indeterminacy, using what we call "hbar-polar…

The density of Bloch electromagnetic states inside a one dimensional photonic crystal (1D PC) is formulated based on its dispersion relations. The formulation applied to any anisotropic medium with known dispersion relations and…