Compact endomorphisms of $H^∞(D)$

Tom 136 / 1999

Joel F. Feinstein, 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.


  • Joel F. Feinstein

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