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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
##### Keywords:
invariant subspaces; Hardy space
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