# zbMATH — the first resource for mathematics

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
Full Text: