Holomorphic semi-almost periodic functions. (English) Zbl 1198.30051
The authors study the Banach algebra \(A\) of bounded holomorphic functions on the unit disk whose boundary values belong to the algebra of semi-almost periodic functions on the circle. Related algebras are considered, too. Some specific subjects dealt with are: the approximation property (that is, for every compact set \(K\subseteq A\) and every \(\epsilon>0\) there exists a linear operator \(T:A\to A\) of finite rank so that \(||Tx-x||_A<\epsilon\) for every \(x\in K\)) and the corona property of \(A\).
Reviewer: Raymond Mortini (Metz)
MSC:
| 30H05 | Spaces of bounded analytic functions of one complex variable |
| 46J15 | Banach algebras of differentiable or analytic functions, \(H^p\)-spaces |
| 47A58 | Linear operator approximation theory |
Keywords:
approximation property; semi-almost periodic functions; maximal ideal space; bounded analytic functions; corona-propertyReferences:
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