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Compact endomorphisms of \(H^\infty(D)\). (English) Zbl 0936.46041
The authors characterize the compact endomorphisms of the algebra \(H^\infty(\mathbb{D})\) of all bounded analytic functions in the open unit disk \(\mathbb{D}\) and determine their spectra. Several examples are given, showing the difference between composition operators and general endomorphisms on \(H^\infty\).
Reviewer’s remark: The results are well-known. We refer the reader to the doctoral thesis of Udo Klein, published in [Mitt. Math. Semin. Giessen 232, 1-120 (1997)], where the general theory of compact multiplicative operators on uniform algebras is developed.
Reviewer: R.Mortini (Metz)

MSC:
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
47B48 Linear operators on Banach algebras
47B33 Linear composition operators
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