Difference of composition operators on Hardy space

Spectrum and essential spectrum of linear combinations of composition operators on the Hardy space H2

Let -----. For an analytic self-map ---  of --- , Let --- be the composition operator with composite map ---  so that ----. Let ---  be a bounded analytic function on --- . The weighted composition operator ---  is defined by --- . Suppose that ---  is the Hardy space, consisting of all analytic functions defined on --- , whose Maclaurin cofficients are square summable. .....

Norms of Composition Operators on the Hardy Space

Research supported in part by National Science Foundation grant DMS-9401206. Appel and Thrall were supported by the Foundation's REU program for work they performed as undergraduate assistants to Bourdon. We show that the norm of a composition operator on the classical Hardy space H2 cannot be computed using only the set of H2 reproducing kernels, answering a question raised by Cowen and MacCluer.

Bilateral composition operators on vector-valued Hardy spaces

Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$‎. ‎We investigate some operator theoretic properties of‎ ‎bilateral composition operator $C_{ph‎, ‎T}‎: ‎f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq‎ ‎+infty$.‎ ‎Compactness and weak compactness of $C_{ph‎, ‎T}$ on $H^p(X)$‎ ‎are characterized an...

Generalized composition operators on weighted Hardy spaces

Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane

and Applied Analysis 3 In two main theorems in 20 , the authors proved the following results, which we now incorporate in the next theorem. Theorem A. Assume p ≥ 1 and φ is a holomorphic self-map of Π . Then the following statements true hold. a The operator Cφ : H Π → A∞ Π is bounded if and only if sup z∈Π Im z ( Imφ z )1/p < ∞. 1.8 b The operator Cφ : H Π → B∞ Π is bounded if and only if sup ...