Related papers: Weak compactness and strongly summing multilinear …
We show that if $u$ is a compactly supported distribution on the complex plane such that, for every pair of entire functions $f,g$, \[ \langle u,f\overline{g}\rangle=\langle u,f\rangle\langle u,\overline{g}\rangle, \] then $u$ is supported…
In this paper, we gave a weighted compactness theory for the generalized commutators of vecotor-valued multilinear Calder\'{o}n-Zygmund operators. This was done by establishing a weighted Fr\'{e}chet-Kolmogorov theorem, which holds for…
Letting $E$, $F$ be Banach spaces, the main two results of this paper are the following: (1) If every (linear bounded) operator $E\rightarrow F$ is unconditionally converging, then every polynomial from $E$ to $F$ is unconditionally…
We investigate lineability/spaceability problems within the setting of multilinear summing operators on quasi-Banach sequence spaces. Furthermore, we deal with the contemporary geometric notions of pointwise-lineability and…
We show that every inclusion of von Neumann algebras with a faithful normal conditional expectation has the weak relative Dixmier property. This answers a question of Popa \cite{Po99}. The proof uses an improvement of Ellis' lemma for…
We adopt an operator-theoretic perspective to analyze a class of nonlinear fixed-point iterations and discrete-time dynamical systems. Specifically, we study the Krasnoselskij iteration - at the heart of countless algorithmic schemes and…
The article addresses some open questions about the relations between the topological weak mixing property and the transitivity of the map $f\times f^2 \times...\times f^m$, where $f\colon X\ra X$ is a topological dynamical system on a…
We extend the definition of weak and strong convergence to sequences of Sobolev-functions whose underlying domains themselves are converging. In contrast to previous works, we do so without ever assuming any sort of reference configuration.…
We investigate weak and strong structures for generalized topological spaces, among others products, sums, subspaces, quotients, and the complete lattice of generalized topologies on a given set. Also we introduce $T_{3.5}$ generalized…
In this note we prove an abstract version of a result from 2002 due to Delgado and Pi\~{n}ero on absolutely summing operators. Several applications are presented; some of them in the multilinear framework and some in a completely nonlinear…
We consider operators T : M_0 -> Z and T : M -> Z, where Z is a Banach space and (M_0, M) is a pair of Banach spaces belonging to a general construction in which M is defined by a "big-O" condition and M_0 is given by the corresponding…
We introduce and study a new class of operators that we call disjoint weak Banach-Saks operators. We establish some characterizations of this class of operators by different types of convergence (norm convergence, unbounded order…
We consider the class of multiple Fourier series associated with functions in the Dirichlet space of the polydisc. We prove that every such series is summable with respect to unrestricted rectangular partial sums, everywhere except for a…
Many special classes of simplicial sets, such as the nerves of categories or groupoids, the 2-Segal sets of Dyckerhoff and Kapranov, and the (discrete) decomposition spaces of G\'{a}lvez, Kock, and Tonks, are characterized by the property…
By Zeckendorf's Theorem, every positive integer is uniquely written as a sum of non-adjacent terms of the Fibonacci sequence, and its converse states that if a sequence in the positive integers has this property, it must be the Fibonacci…
Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ for all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact on $L^{p_1}(w_1)$ for some $w_1\in A_{p_1}(\mathbb R^d)$. Then $T$ is…
We present a sufficient condition on sets $E$ and $F$ in $\mathbb{R}^d$ to ensure compactness of Fourier concentration operators by introducing the notion of sets which are very thin at infinity. We are able to show that if the sets $E$ and…
The symmetric Grothendieck polynomials generalize Schur polynomials and are Schur-positive by degree. Combinatorially this is manifested as the generalization of semistandard Young tableaux by set-valued tableaux. We define a (weak)…
A weak formulation is devised for the K(m,n) equation which is a nonlinearly dispersive generalization of the gKdV equation having compacton solutions. With this formulation, explicit weak compacton solutions are derived, including ones…
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…