Abstract. In this article, we define discrete analogue of generalized Hardy spaces and its separable subspace on a homogenous rooted tree and study some of its properties such as completeness, inclusion relations with other spaces, separability, growth estimate for functions in these spaces and their consequences. Equivalent conditions for multiplication operators to be bounded and compact are also obtained. Furthermore, we discuss about point spectrum, approximate point spectrum and spectrum of multiplication operators and discuss when a multiplication operator is an isometry.
Abstract. In this paper, we study the basic properties such as boundedness and compactness of composition operators on discrete analogue of generalized Hardy space defined on a homogeneous rooted tree. Also, we compute the operator norm of composition operator when inducing symbol is automorphism of a homogenous tree.
The aim of this paper is to answer the following question concerning invariant subspaces of composition operators: characterize φ, holomorphic self maps of D, and inner functions θ∈H∞(D) such that the Beurling type invariant subspace θH2 is an invariant subspace for Cφ. We prove the following result: Cφ(θH2)⊆θH2 if and only if θ∘φθ∈S(D). This classification also allows us to recover or improve some known results on Beurling type invariant subspaces of composition operators.
In [16], the present authors initiated the study of composition operators on discrete analogue of generalized Hardy space T p defined on a homogeneous rooted tree. In this article, we give equivalent conditions for the composition operator C φ to be bounded on T p and on T p,0 spaces and compute their operator norm. We also characterize invertible composition operators as well as isometric composition operators on T p and on T p,0 spaces. Also, we discuss the compactness of C φ on T p and finally prove there are no compact composition operators on T p,0 spaces.2000 Mathematics Subject Classification. Primary: 05C05, 37E25, 47B33, 47B38; Secondary: 30H10, 46B50.
In this article, we study the weighted composition operators preserving the class P α of analytic functions subordinate to 1+αz 1−z for |α| ≤ 1, α = −1. Some of its consequences and examples for some special cases are presented.2000 Mathematics Subject Classification. Primary: 47B38, 47B33, 30C80; Secondary: 37C25.
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