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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Completely continuous Hankel operators on $ H\sp \infty$ and Bourgain algebras


Authors: Joseph A. Cima, Svante Janson and Keith Yale
Journal: Proc. Amer. Math. Soc. 105 (1989), 121-125
MSC: Primary 30D55; Secondary 46J15, 47B35
MathSciNet review: 931727
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Abstract: Let $ {({H^\infty })_b}$ be the Bourgain algebra of $ {H^\infty } \subset {L^\infty }$. We prove $ {({H^\infty })_b} = {H^\infty } + C$. In particular if $ f \in {L^\infty }$ then the Hankel operator $ {H_f}$ is a compact map of $ {H^\infty }$ into BMO iff whenever $ {f_n} \to 0$ weakly in $ {H^\infty }$, then $ \operatorname{dist}{(}f{f_n},{H^\infty }) \to 0$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0931727-6
PII: S 0002-9939(1989)0931727-6
Keywords: Bourgain algebra, Hankel operator
Article copyright: © Copyright 1989 American Mathematical Society