Hedenmalm, Per Jan Håkan An invariant supspace of the Bergman space having the codimension two property. (English) Zbl 0783.30040 J. Reine Angew. Math. 443, 1-9 (1993). A constructive example is given of a \(z\)-invariant subspace \(J\) of the Bergman space \(L^ 2_ a(\mathbb{D})\) such that \(zJ\) has codimension 2 in \(J\). The construction, which is based on Kristian Seip’s characterization of sampling and interpolating sequences for the space \(L^ 2_ a(\mathbb{D})\), is then generalized to obtain, for each integer \(n\geq 2\), a \(z\)-invariant subspaces \(J\) such that \(zJ\) has codimension \(n\) in \(J\). Reviewer: H.Hedenmalm (Uppsala) Cited in 3 ReviewsCited in 29 Documents MSC: 30H05 Spaces of bounded analytic functions of one complex variable 47B99 Special classes of linear operators 46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) 46C99 Inner product spaces and their generalizations, Hilbert spaces Keywords:sampling sequences; Bergman space; interpolating sequences PDFBibTeX XMLCite \textit{P. J. H. Hedenmalm}, J. Reine Angew. Math. 443, 1--9 (1993; Zbl 0783.30040) Full Text: DOI Crelle EuDML