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Compact homomorphisms between algebras of analytic functions

Tom 123 / 1997

Studia Mathematica 123 (1997), 235-247 DOI: 10.4064/sm-123-3-235-247

Streszczenie

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.

• Richard Aron

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