Composition operators on the Dirichlet space and related problems.
Composition operators on vector-valued Hardy spaces.
Composition operators on W 1 X are necessarily induced by quasiconformal mappings
Let Ω ⊂ ℝn be an open set and X(Ω) be any rearrangement invariant function space close to L q(Ω), i.e. X has the q-scaling property. We prove that each homeomorphism f which induces the composition operator u ↦ u ℴ f from W 1 X to W 1 X is necessarily a q-quasiconformal mapping. We also give some new results for the sufficiency of this condition for the composition operator.
Cyclic behavior of linear fractional composition operators.
Cyclic Blaschke products for composition operators.
Cyclicity of the adjoint of weighted composition operators on the Hilbert space of analytic functions
In this paper, we discuss the hypercyclicity, supercyclicity and cyclicity of the adjoint of a weighted composition operator on a Hilbert space of analytic functions.
Differences of composition operators on the space of bounded analytic functions in the polydisc.
Differences of generalized weighted composition operators between growth spaces
Let φ and ψ be analytic self-maps of 𝔻. Using the pseudo-hyperbolic distance ρ(φ,ψ), we completely characterize the boundedness and compactness of the difference of generalized weighted composition operators between growth spaces.
Differences of weighted composition operators from Hardy space to weighted-type spaces on the unit ball
In this paper, we limit our analysis to the difference of the weighted composition operators acting from the Hardy space to weighted-type space in the unit ball of , and give some necessary and sufficient conditions for their boundedness or compactness. The results generalize the corresponding results on the single weighted composition operators and on the differences of composition operators, for example, M. Lindström and E. Wolf: Essential norm of the difference of weighted composition operators....
Differences of weighted composition operators on .
Differences of weighted compostion operators.
Disjoint hypercyclic operators
We introduce the concept of disjoint hypercyclic operators. These are operators performing the approximation of any given vectors with a common subsequence of iterates applied on a common vector. The notion is extended to sequences of operators, and applied to composition operators and differential operators on spaces of analytic functions.
Distances between composition operators.
Composition operators Cφ induced by a selfmap φ of some set S are operators acting on a space consisting of functions on S by composition to the right with φ, that is Cφf = f º φ. In this paper, we consider the Hilbert Hardy space H2 on the open unit disk and find exact formulas for distances ||Cφ - Cψ|| between composition operators. The selfmaps φ and ψ involved in those formulas are constant, inner, or analytic selfmaps of the unit disk fixing the origin.
Dynamics of composition operators in analytic functional Hilbert spaces. (Dinámica de operadores de composición en espacios de Hilbert funcionales analíticos.)
Embedding theorems for Müntz spaces
We discuss boundedness and compactness properties of the embedding , where is the closed linear span of the monomials in and is a finite positive Borel measure on the interval . In particular, we introduce a class of “sublinear” measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences . Finally, we show how one can recapture some of Al Alam’s results on boundedness and the essential norm of weighted composition operators from ...
Essential norm of the difference of composition operators on Bloch space
Let and be holomorphic self-maps of the unit disk, and denote by , the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators from Bloch spaces to Bloch spaces in the unit disk. Compactness of the difference is also characterized.
Essential norm of weighted composition operator between -Bloch space and -Bloch space in polydiscs.
Essential norm of weighted composition operators on the Dirichlet space.
In this paper, we characterize boundedness and compactness of weighted composition operators on the Dirichlet space and obtain the estimates for the essential norm.
Essential normality for certain finite linear combinations of linear-fractional composition operators on the Hardy space
In 1999 Nina Zorboska and in 2003 P. S. Bourdon, D. Levi, S. K. Narayan and J. H. Shapiro investigated the essentially normal composition operator , when is a linear-fractional self-map of . In this paper first, we investigate the essential normality problem for the operator on the Hardy space , where is a bounded measurable function on which is continuous at each point of , , and is the Toeplitz operator with symbol . Then we use these results and characterize the essentially normal...
Essential norms of weighted composition operators between Hardy spaces and for 1 ≤ p,q ≤ ∞
We complete the different cases remaining in the estimation of the essential norm of a weighted composition operator acting between the Hardy spaces and for 1 ≤ p,q ≤ ∞. In particular we give some estimates for the cases 1 = p ≤ q ≤ ∞ and 1 ≤ q < p ≤ ∞.