Compact endomorphisms of $H^∞(D)$
Tom 136 / 1999
Studia Mathematica 136 (1999), 87-90 DOI: 10.4064/sm-136-1-87-90
Compact composition operators on $H^∞(G)$, where G is a region in the complex plane, and the spectra of these operators were described by D. Swanton ( Compact composition operators on B(D), Proc. Amer. Math. Soc. 56 (1976), 152-156). In this short note we characterize all compact endomorphisms, not necessarily those induced by composition operators, on $H^∞(D)$, where D is the unit disc, and determine their spectra.