Local spectral theory of endomorphisms of the disk algebra

Let A(D) denote the disk algebra. Every endomorphism of A(D) is induced by some φ (…) A(D) with ║φ║ ≤ 1. In this paper, it is shown that if φ is not an automorphism of D 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.

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Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.