Pairs of inner projections and two applications

Orthogonal projections onto closed subspaces of H2(Dn) of the form phi H2(Dn) for inner functions phi on Dn are referred to as inner projections, where H2(Dn) denotes the Hardy space over the open unit polydisc Dn. In this paper, we classify pairs of commuting inner projections. We also present two seemingly independent applications: the first is an answer to a question posed by R. G. Douglas, and the second is a complete classification of partially isometric truncated Toeplitz operators with inner symbols on Dn. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates the classification of inner projections and their relationships with other problems. Two independent applications are presented as well.