Compact homomorphisms between algebras of analytic functions

Richard Aron; Pablo Galindo; Mikael Lindström

Studia Mathematica (1997)

  • Volume: 123, Issue: 3, page 235-247
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Aron, Richard, Galindo, Pablo, and Lindström, Mikael. "Compact homomorphisms between algebras of analytic functions." Studia Mathematica 123.3 (1997): 235-247. <http://eudml.org/doc/216391>.

@article{Aron1997,
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.},
author = {Aron, Richard, Galindo, Pablo, Lindström, Mikael},
journal = {Studia Mathematica},
keywords = {Tsirelson space; uniform algebra of all bounded analytic functions in the open unit disk; weakly compact algebra endomorphism; composition operators; compact multiplicative operators},
language = {eng},
number = {3},
pages = {235-247},
title = {Compact homomorphisms between algebras of analytic functions},
url = {http://eudml.org/doc/216391},
volume = {123},
year = {1997},
}

TY - JOUR
AU - Aron, Richard
AU - Galindo, Pablo
AU - Lindström, Mikael
TI - Compact homomorphisms between algebras of analytic functions
JO - Studia Mathematica
PY - 1997
VL - 123
IS - 3
SP - 235
EP - 247
AB - 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.
LA - eng
KW - Tsirelson space; uniform algebra of all bounded analytic functions in the open unit disk; weakly compact algebra endomorphism; composition operators; compact multiplicative operators
UR - http://eudml.org/doc/216391
ER -

References

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