We study the asymptotic behaviour of the powers T of a composition operator T on an arbitrary Banach space X of holomorphic functions on the open unit disc D of C. We show that for composition operators, one has the following dichotomy: either the powers converge uniformly or they do not converge even strongly. We also show that uniform convergence of the powers of an operator T ∈ L(X) is very ...

We study the recent proposal of Goyal and Egenhofer who presented a model for qualitative spatial reasoning about cardinal directions. Our approach is formal and complements the presentation of Goyal and Egenhofer. We focus our efforts on the composition operator for two cardinal direction relations. We consider two interpretations of the composition operator: consistency-based and existential ...

First, we introduce some basic notation which is used in this paper. Throughout the entire paper, the unit disk in the finite complex plane C will be denoted by D. H D will denote the space of all analytic functions on D. Every analytic self-map φ of the unit disk D induces through composition a linear composition operator Cφ fromH D to itself. It is a well-known consequence of Littlewood’s sub...

Let φ and ψ be holomorphic maps on such that φ( ) ⊂ . Let Cφ,Mψ and D be the composition, multiplication and differentiation operators, respectively. In this paper, we consider linear operators induced by products of these operators from Bergman-Nevanlinna spaces AβN to Bloch-type spaces. In fact, we prove that these operators map AβN compactly into Bloch-type spaces if and only if they map A β...

Fuzzy operators are an essential tool in many fields and the operation of composition is often needed. In general, composition is not a commutative operation. However, it is very useful to have operators for which the order of composition does not affect the result. In this paper, we analyze when permutability appears. That is, when the order of application of the operators does not change the ...

We give a backward jeu de taquin slide analogue on semistandard reverse composition tableaux. These tableaux were first studied by Haglund, Luoto, Mason and van Willigenburg when defining quasisymmetric Schur functions. Our algorithm for performing backward jeu de taquin slides on semistandard reverse composition tableaux results in a natural operator on compositions that we call the jdt operat...

We consider the completely positive map on the Toeplitz operator system given by conjugation by a composition operator; that is, we analyze operators of the form C∗ φTfCφ We prove that every such operator is weakly asymptotically Toeplitz, and compute its asymptotic symbol in terms of the Aleksandrov-Clark measures for φ. When φ is an inner function, this operator is Toeplitz, and we show under...

An algebra of bounded linear operators on a Hilbert space is called strongly compact whenever each of its bounded subsets is relatively compact in the strong operator topology. The concept is most commonly studied for two algebras associated with a single operator T : the algebra alg(T ) generated by the operator, and the operator’s commutant com(T ). This paper focuses on the strong compactnes...