Compact homomorphisms between algebras of analytic functions
Volume 123 / 1997
Studia Mathematica 123 (1997), 235-247
DOI: 10.4064/sm-123-3-235-247
Abstract
We prove that every weakly compact multiplicative linear continuous map from $H^∞(D)$ into $H^∞(D)$ is compact. We also give an example which shows that this is not generally true for uniform algebras. Finally, we characterize the spectra of compact composition operators acting on the uniform algebra $H^∞(B_E)$, where $B_E$ is the open unit ball of an infinite-dimensional Banach space E.
