Structure of subalgebras between 𝐿^{∞} and 𝐻^{∞}

Chang, Sun Yung A.

doi:10.1090/S0002-9947-1977-0433213-5

Structure of subalgebras between $L^{\infty }$ and $H^{\infty }$
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Trans. Amer. Math. Soc. 227 (1977), 319-332 Request permission

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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