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Large Bergman spaces: invertibility, cyclicity, and subspaces of arbitrary index

Alexander Borichev·Hakan Hedenmalm·Alexander Volberg
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Abstract

In a wide class of weighted Bergman spaces, we construct invertible non-cyclic elements. These are then used to produce z-invariant subspaces of index higher than one. In addition, these elements generate nontrivial bilaterally invariant subspaces in anti-symmetrically weighted Hilbert spaces of sequences.

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Alexander Borichev, Hakan Hedenmalm, Alexander Volberg. 2003-04-22. Large Bergman spaces: invertibility, cyclicity, and subspaces of arbitrary index. https://arxiv.org/abs/math/0304318

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