Related papers: SB-property on metric structures

Let $\mathcal{B}(H)$ be the bounded, linear operators on a separable Hilbert space equipped with the norm topology. A property is called typical if the set of operators fulfilling the property is co-meager. We show that having non-empty…

Based on an idea of Y. P\'eresse and some results of Maltcev, Mitchell and Ru\v{s}kuc, we present sufficient conditions under which the endomorphism monoid of a countably infinite ultrahomogeneous first-order structure has the Bergman…

Motivated by the foundational result that a monomial complete intersection has the strong Lefschetz property (SLP) in characteristic zero, it is natural to ask when monomial almost complete intersections have the SLP. In this paper, using…

Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous frames for tensor product of Hilbert spaces. This includes, for example,…

We say that a smooth normed space $X$ has a property (SL), if every mapping $f:X \to X$ preserving the semi-inner product on $X$ is linear. It is well known that every Hilbert space has the property (SL) and the same is true for every…

The Schur-Horn theorem is a well-known result that characterizes the relationship between the diagonal elements and eigenvalues of a symmetric (Hermitian) matrix. In this paper, we extend this theorem by exploring the eigenvalue…

In this paper we introduce the notion of property $(BR)$ and property $(BgR)$ for bounded linear operators defined on an infinite-dimensional Banach space. These properties in connection with Weyl type theorems and in the frame of polaroid…

The Bel-Robinson tensor contains many nice mathematical properties and its dominant energy condition is desirable for describing the positive gravitational energy. The dominant property is a basic requirement for the quasi-local mass, i.e.,…

The paper is concerned with completeness property of rank one perturbations of unperturbed operators generated by special boundary value problems (BVP) for the following $2 \times 2$ system \begin{equation} L y = -i B^{-1} y' + Q(x) y =…

A spectral theory of linear operators on a rigged Hilbert space is applied to Schr\"odinger operators with exponentially decaying potentials and dilation analytic potentials. The theory of rigged Hilbert spaces provides a unified approach…

Let $Z$ be a fixed separable operator space, $X\subset Y$ general separable operator spaces, and $T:X\to Z$ a completely bounded map. $Z$ is said to have the Complete Separable Extension Property (CSEP) if every such map admits a completely…

We show in this paper that a certain class of normed modules over the algebra of all bounded operators on a Hilbert space possesses a homological property which is a kind of a functional-analytic version of the standard algebraic property…

A field extension $L/K$ of characteristic $p > 0$ is formally \'etale if and only if the relative Frobenius of $L/K$ is an isomorphism. Inspired by this classical result, we explore whether the formally \'etale property for a map $R \to S$…

We prove a Tb Theorem that characterizes all Calderon-Zygmund operators that extend compactly on L^p(R^n), 1<p<\infty . The result, whose proof does not require the property of accretivity, can be used to prove compactness of the Double…

In this paper, we study the stability of Property $(UW_E)$ under commuting finite rank perturbation in terms of spectrum induced by consistent in invertibility for operators and a variant of upper semi-Weyl spectrum. Also we discuss the…

In this paper, we use a new method to solve a long-standing problem. More specifically, we show that the Beurling-type theorem holds in the Bergman space $A^2_\alpha(D)$ for any $-1<\alpha < +\infty$. That is, every invariant subspace $H$…

We establish a strong unique continuation property for the subelliptic Baouendi operator under the presence of zero-order perturbations satisfying an almost Hardy-type growth condition. In particular, the admissible class includes both…

Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed…

We characterize diagonals of unbounded self-adjoint operators on a Hilbert space H that have only discrete spectrum, i.e., with empty essential spectrum. Our result extends the Schur-Horn theorem from a finite dimensional setting to an…

In this paper, we study one of the fundamental notions in dynamical systems, the shadowing of invertible (bounded and linear) operators on a Hilbert space. Although the problem of finding a spectral characterization for shadowing has been…