Local spectral theory of endomorphisms of the disk algebra

Demonstratio mathematica

article

Shailesh Trivedi¹  Harish Chandra¹ 

[1] Department of Mathematics and DST-CIMS, Banaras Hindu University

关键词: composition operator;    decomposability and super-decomposability;    endomorphism;    local spectrum;    Single Valued Extension Property;   

DOI  :  10.1515/dema-2016-0009

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

Let A (?) denote the disk algebra. Every endomorphism of A (?) is induced by some ϕ ∈ A (?) with ‖ ϕ ‖ ≤ 1. In this paper, it is shown that if ϕ is not an automorphism of ? and ϕ has a fixed point in the open unit disk then the endomorphism induced by ϕ is decomposable if and only if the fixed set of ϕ is singleton. Further, we determine the local spectra of the endomorphism induced by ϕ in the cases when the fixed set of ϕ either includes unit circle or is a singleton.

【 授权许可】

CC BY