泛函分析

In this paper, we provide proofs for the analytic characterization theorems of the operator symbols utilizing the characterization theorem for the Mittag-Leffler distribution space.We work out examples which can be interpreted as integral…

The classical concept of Fenchel conjugation is tailored to extended real-valued functions defined on linear spaces. In this paper we generalize this concept to functions defined on arbitrary sets that do not necessarily bear any structure…

We study the ``no-dimensional'' analogue of Helly's theorem in Banach spaces. Specifically, we obtain the following no-dimensional Helly-type results for uniformly convex Banach spaces: Helly's theorem, fractional Helly's theorem, colorful…

We show that if a separable Banach space has Kalton's property $(M^\ast)$, then all $\varepsilon$-Szlenk derivations of the dual unit ball are balls, however, in the case of the dual of Baernstein's space, all those Szlenk derivations are…

Property~(A) is a week symmetry condition that plays a fundamental role in the characterization of greedy-type bases in the isometric case, i.e., when the constants involved in the study of the efficiency of the thresholding greedy…

The aim of this paper is twofold. On the one hand, we manage to identify Banach-valued Hardy spaces of analytic functions over the disc $\mathbb{D}$ with other classes of Hardy spaces, thus complementing the existing literature on the…

Consider a bounded symmetric domain $\Omega$ with a finite pseudo-reflection group acting on it as a subgroup of the group of automorphisms. This gives rise to quotient domains by means of basic polynomials $\theta$ which by virtue of being…

Harmonic synthesis describes translation invariant linear spaces of continuous complex valued functions on locally compact abelian groups. The basic result due to L. Schwartz states that such spaces on the reals are topologically generated…

We show that the Carath\'{e}odory number of the joint numerical range of $d$ many bounded self-adjoint operators is at most $d-1$, and even at most $d-2$ if the underlying Hilbert space has dimension at least $3$. This extension of the…

Let $A$ be an $m\times m$ complex matrix and let $\lambda _1, \lambda _2, \ldots , \lambda _m$ be the eigenvalues of $A$ arranged such that $|\lambda _1|\geq |\lambda _2|\geq \cdots \geq |\lambda _m|$ and for $n\geq 1,$ let $s^{(n)}_1\geq…

We prove a Wiener-type theorem for arcs in the unit circle which concerns express the measure of an arc in the unit circle via the measure's Fourier coefficients. Then we use it to give the Fourier series of the Cantor and to compute the…

Recently K.-G. Grosse-Erdmann and D. Papathanasiou described hypercyclic shifts in weighted spaces on directed trees. In this note we discuss several simple examples of graphs which are not trees, e.g., the lattice graphs, and study…

In this paper, we introduce the concept of continuous $g-$atomic subspace for a bounded linear operator and gives several useful continuous resolution of the identity operator on a Hilbert space by implies the theory of continuous…

We present a short elementary proof of the Gearhart-Pr\"uss theorem for bounded $C_0$-semigroups on Hilbert spaces.

We prove a continuous-parameter version of the recent theorem of Katznelson-Tzafiri type for power-bounded operators which have a bounded calculus for analytic Besov functions. We also show that the result can be extended to some operators…

This paper is a survey article on developments arising from a theorem proved by Katznelson and Tzafriri in 1986 showing that $\lim_{n\to\infty} \|T^n(I-T)\| =0$ if $T$ is a power-bounded operator on a Banach space and $\sigma(T) \cap \T…

In this paper, we study a few versions of the uncertainty principle for the short-time Fourier transform on the lattice $\mathbb Z^n \times \mathbb T^n$. In particular, we establish the uncertainty principle for orthonormal sequences,…

Let $T$ be a power-bounded operator on a Banach space $X$, $\mathcal{A}$ be a Banach algebra of bounded holomorphic functions on the unit disc $\mathbb{D}$, and assume that there is a bounded functional calculus for the operator $T$, so…

The purpose of this paper is concerned with the approximate solution of split equality problems. We introduce two types of algorithms and a new self-adaptive stepsize without prior knowledge of operator norms. The corresponding strong…

Only in the last fifteen years or so has the notion of semi-uniform stability, which lies between exponential stability and strong stability, become part of the asymptotic theory of $C_0$-semigroups. It now lies at the very heart of modern…