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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Structure of subalgebras between $ L\sp{\infty }$ and $ H\sp{\infty }$


Author: Sun Yung A. Chang
Journal: Trans. Amer. Math. Soc. 227 (1977), 319-332
MSC: Primary 46J15; Secondary 30A98
MathSciNet review: 0433213
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Abstract: Let B be a closed subalgebra of $ {L^\infty }$ of the unit circle which contains $ {H^\infty }$ properly. Let $ {C_B}$ be the $ {C^\ast}$-algebra generated by the inner functions that are invertible in B. It is shown that the linear span $ {H^\infty } + {C_B}$ is equal to B. Also, a closed subspace (called $ VM{O_B}$) of BMO (space of functions of bounded mean oscillation) is identified to which B bears the same relation as $ {L^\infty }$ does to BMO.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0433213-5
PII: S 0002-9947(1977)0433213-5
Article copyright: © Copyright 1977 American Mathematical Society