Structure of subalgebras between l00 and h

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Abstract

Let B be a closed subalgebra of L∞ of the unit circle which contains L∞ properly. Let CB be the C*-algebra generated by the inner functions that are invertible in B. It is shown that the linear span H∞ + CB is equal to B. Also, a closed subspace (called VMOB) of BMO (space of functions of bounded mean oscillation) is identified to which B bears the same relation as L∞ does to BMO.

Original languageEnglish (US)
Pages (from-to)319-332
Number of pages14
JournalTransactions of the American Mathematical Society
Volume227
DOIs
StatePublished - Jan 1 1977
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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