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Projections and minimal invariant subspaces in the Hardy space over the bidisk

  • Marcos dos Santos Ferreira
  • João Marcos Ribeiro do Carmo
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Abstract

We study the rigidity of the orthogonal projections Pn:H2(𝔻2)→ Hn, where H2(𝔻2)=⨁n=0∞Hn and each Hn=H2(z)wn is a reducing subspace for Tz, and we derive properties of the minimal invariant subspaces of Tz*. Our main result establishes that the nonzero projections of a minimal invariant subspace onto the one-variable Hardy space share a common tz*-invariant structure. Furthermore, we relate the results obtained to an approach to the invariant subspace problem.

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Cite

BibTeXRIS
BibTeX
@misc{ferreira2026projections,
  title = {{Projections and minimal invariant subspaces in the Hardy space over the bidisk}},
  author = {Marcos dos Santos Ferreira and João Marcos Ribeiro do Carmo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19311},
  eprint = {2609.19311},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19311},
}
RIS
TY  - UNPB
TI  - Projections and minimal invariant subspaces in the Hardy space over the bidisk
AU  - Marcos dos Santos Ferreira
AU  - João Marcos Ribeiro do Carmo
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.19311
UR  - https://arxiv.org/abs/2609.19311
AB  - We study the rigidity of the orthogonal projections P_n:H^2(𝔻^2)→ H_n, where H^2(𝔻^2)=⨁_n=0^∞H_n and each H_n=H^2(z)w^n is a reducing subspace for T_z, and we derive properties of the minimal invariant subspaces of T_z^*. Our main result establishes that the nonzero projections of a minimal invariant subspace onto the one-variable Hardy space share a common t_z^*-invariant structure. Furthermore, we relate the results obtained to an approach to the invariant subspace problem.
ER  -