Compact endomorphisms of H infinity of D

Details Compact endomorphisms of H infinity of D Compact endomorphisms of H infinity of D

1998-10-21

arxiv.org/abs/math/9810131v1

Mathematics

Functional Analysis

4 pages, LaTeX

Scientific paper

When G is a region in the complex plane, compact composition operators on the uniform algebra of bounded analytic functions on G and the spectra of these operators were described by D. Swanton, Compact composition operators on B(D), Proc. Amer. Math. Soc. 56 (1976). In this short note we characterize all compact endomorphisms, not necessarily those induced by composition operators, on the uniform algebra of bounded analytic functions on the open unit disc, and determine their spectra. This research was supported by EPSRC grant GR/M31132

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