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We establish criteria for the stability of the essential spectrum for unbounded operators acting in Banach modules. The applications cover operators acting on sections of vector fiber bundles over non-smooth manifolds or locally compact…
As it was shown by Shen, the Riesz transforms associated to the Schr\"odinger operator $L=-\Delta + V$ are not bounded on $L^p(\mathbb{R}^d)$-spaces for all $p, 1<p<\infty$, under the only assumption that the potential satisfies a reverse…
Messages in communication networks often are considered as "discrete" taking values in some finite alphabet (e.g. a finite field). However, if we want to consider for example communication based on analogue signals, we will have to consider…
The absolutely continuous spectrum of one-dimensional Schr\"odinger operators is proved to be stable under perturbation by potentials satisfying mild decay conditions. In particular, the absolutely continuous spectrum of free and periodic…
We give embedding theorems for weighted Bergman-Orlicz spaces on the ball and then apply our results to the study of composition operators in this context. As one of the motivations of this work, we show that there exist some weighted…
Suppose $X$ is a locally solid vector lattice. It is known that there are several non-equivalent spaces of bounded operators on $X$. In this paper, we consider some situations under which these classes of bounded operators form locally…
In this article we introduce a new scale of weighted Orlicz-Sobolev sequence spaces generated by a class of suitable Orlicz functions and prove various continuity and compactness criteria for them. In a nutshell, continuity is a consequence…
We revisit the results of Kitson and Timoney \emph{[J.~Math.~Anal.~Appl.~\textbf{378} (2011), 680--686]} on the spaceability of complements of operator ranges, extending one of their main theorems to the general Fr\'echet setting. In…
New approaches to the study of stability of solutions of Set Differential Equations (SDEs) based on convex geometry and the theory of mixed volumes were proposed. The stability of the forms of program solutions of linear SDEs with a stable…
Several recent papers were devoted to various modifications of limited, Grothendieck, and Dunford--Pettis operators, etc., through involving the Banach lattice structure. In the present paper, it is shown that many of these operators appear…
We prove well-posedness for some abstract differential equations of the first order. Our result covers the usual case of Lipschitz composition operators. It also contains the case of some integro-differential operators acting on spaces with…
We establish a relationship between Schreiner's matrix regular operator space and Werner's (nonunital) operator system. For a matrix ordered operator space $V$ with complete norm, we show that $V$ is completely isomorphic and complete order…
The uncertainty principle lemma for the Laplacian on Euclidean spaces shows the borderline-behavior of a potential for the following question : whether the Schr\"odinger operator has a finite or infinite number of the discrete pectrum. In…
We introduce a class of (tuples of commuting) unbounded operators on a Banach space, admitting smooth functional calculi, that contains all operators of Helffer-Sj\"ostrand type and is closed under the action of smooth proper mappings.…
In this article, we completely classify invariant subspaces of finite-rank perturbations of a class of Toeplitz operators on vector-valued Hardy spaces. As a consequence, in the vector-valued setting, we characterize invariant and almost…
We introduce and study the concept of generating function for natural elements in a Dedekind complete Riesz space equipped with a conditional expectatnion operator. This allows to study discrete processes in free-measure setting. In…
While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…
The difficulty for solving ill-posed linear operator equations in Hilbert space is reflected by the strength of ill-posedness of the governing operator, and the inherent solution smoothness. In this study we focus on the ill-posedness of…
We present a generalization of the Radon-Riesz property to sequences of continuous functions with values in uniformly convex and uniformly smooth Banach spaces.
Our goal in this paper is to extend the theory of quasi-exactly solvable Schrodinger operators beyond the Lie-algebraic class. Let $\cP_n$ be the space of n-th degree polynomials in one variable. We first analyze "exceptional polynomial…