Compactness of products and commutators of inner projections

Summary · qwen2.5:32b

The paper characterizes the compactness of products and commutators of inner projections in Hardy spaces over unit disks and polydisks, using Douglas algebra for single-variable cases. It identifies a rigidity phenomenon where on the bidisc, the product of two inner projections is compact only if it has finite rank, contrasting with triviality in higher-dimensional polydiscs.

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Exploring the compactness of products and commutators of inner projections on Hardy spaces over the unit disk and polydisc.

Excerpt

arXiv:2604.22284v3 Announce Type: replace Abstract: In this paper, we study the compactness of the product and the commutator of two inner projections on the Hardy spaces over the unit disk and the polydisc. For the single-variable case, we provide a complete characterization of the compactness of the commutator of two inner projections by means of Douglas algebra. In the multivariable setting, we discover a rigidity phenomenon: on the bidisc, the product of two inner projections is compact if and only if it has finite rank, whereas on the polydisc of dimension strictly greater than two, any such compact product must be trivial.