Ranks of fringe operators on finite Rudin type invariant subspaces. (English) Zbl 1518.47013
Summary: Let \(\mathcal{M}\) be a finite Rudin type invariant subspace of the Hardy space over the bidisk with variables \(z, w\). In this paper we determine the rank of the fringe operator \(\mathcal{F}_z\) on \(\mathcal{M} \ominus w \mathcal{M}\).
MSC:
| 47A15 | Invariant subspaces of linear operators |
| 32A35 | \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables |
| 47B37 | Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) |
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