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pro vyhledávání: '"47B33"'
Let $H^\infty$ denotes the algebra of all bounded analytic functions on the unit disk. It is well-known that every (algebra) automorphism of $H^\infty$ is a composition operator induced by disc automorphism. Maurya et al., (J. Math. Anal. Appl. 530 :
Externí odkaz:
http://arxiv.org/abs/2412.03245
Autor:
Flores, Gonzalo, Jung, Mingu, Lancien, Gilles, Petitjean, Colin, Procházka, Antonín, Quilis, Andrés
We show that several operator ideals coincide when intersected with the class of linearizations of Lipschitz maps. In particular, we show that the linearization $\hat{f}$ of a Lipschitz map $f:M\to N$ is Dunford-Pettis if and only if it is Radon-Niko
Externí odkaz:
http://arxiv.org/abs/2411.08369
This paper is concerned with universality properties of composition operators $C_f$, where the symbol $f$ is given by a transcendental entire function restricted to parts of its Fatou set. We determine universality of $C_f$ when $f$ is restricted to
Externí odkaz:
http://arxiv.org/abs/2409.16260
We give a complete characterisation of the linear isometries of ${\rm Hol}(\Omega)$, where $\Omega$ is the half-plane, the complex plane or an annulus centered at 0 and symmetric to the unit circle. Moreover, we introduce new techniques to describe t
Externí odkaz:
http://arxiv.org/abs/2409.16105
Let $\varphi$ be a holomorphic self map of the bidisc that is Lipschitz on the closure. We show that the composition operator $C_{\varphi}$ is compact on the Bergman space if and only if $\varphi(\overline{\mathbb{D}^2})\cap \mathbb{T}^2=\emptyset$ a
Externí odkaz:
http://arxiv.org/abs/2409.09529
V. Matache (J. Operator Theory 73(1):243--264, 2015) raised an open problem about characterizing composition operators $C_{\phi}$ on the Hardy space $H^2$ and nonzero singular measures $\mu_1$, $\mu_2$ on the unit circle such that $C_{\phi}({S_{\mu_1
Externí odkaz:
http://arxiv.org/abs/2408.09759
Autor:
Bes, Juan, Foster, Christopher
We study the dynamic behaviour of (weighted) composition operators on the space of holomorphic functions on a plane domain. Any such operator is hypercyclic if and only if it is topologically mixing, and when the symbol is automorphic, such an operat
Externí odkaz:
http://arxiv.org/abs/2408.05600
We introduce a class of linear bounded invertible operators on Banach spaces, called shift operators, which comprises weighted backward shifts and models finite products of weighted backward shifts and dissipative composition operators. We classify v
Externí odkaz:
http://arxiv.org/abs/2407.20890
We establish complete characterizations of the notion of Li-Yorke chaos for weighted composition operators on $C_0(X)$ spaces and on $L^p(\mu)$ spaces. As a consequence, we obtain simple characterizations of the Li-Yorke chaotic weighted shifts on $c
Externí odkaz:
http://arxiv.org/abs/2407.19091
Autor:
Beauduin, Kei
In this paper, we explore the effectiveness of almost purely operational methods in the study of umbral calculus. To accomplish this goal, we systematically reconstruct the theory operationally, offering new proofs and results throughout. Our approac
Externí odkaz:
http://arxiv.org/abs/2407.16348