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Invariant subspaces of the operator of multiplication by z in the space \(E_ p\) in a multiply connected domain. (Russian. English summary) Zbl 0722.47031
The paper contains a generalization of some results, due to Hitt and Sarason, about the form of invariant subspaces (for the multiplication by z) in the Hardy space \(E^ 2(G)\) over a multiply connected domain G. The author deals with the general case of \(E^ p(G)\), \(1\leq p\leq \infty\). However more precise results are obtained for \(p=2\), under the assumption of analyticity of \(\partial G.\)
The method of proofs is based on the technique (introduced earlier by B. Solomjak) of gluing up of the Cauchy integrals. This permits to obtain a detailed description of the set of all invariant subspaces in \(E^ 2(G)\).
Reviewer: J.Janas (Kraków)

MSC:
47B38 Linear operators on function spaces (general)
46E20 Hilbert spaces of continuous, differentiable or analytic functions
47A15 Invariant subspaces of linear operators
30D55 \(H^p\)-classes (MSC2000)
46H15 Representations of topological algebras
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