Isometric dilations and Beurling quotient modules

@misc{das2026isometric,
  title = {{Isometric dilations and Beurling quotient modules}},
  author = {B. Krishna Das and Shubham Rastogi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18222},
  eprint = {2610.18222},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18222},
}

TY  - UNPB
TI  - Isometric dilations and Beurling quotient modules
AU  - B. Krishna Das
AU  - Shubham Rastogi
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18222
UR  - https://arxiv.org/abs/2610.18222
AB  - In \cite{Dan-Guo}, the authors provided a characterization of all sequences of doubly commuting pure contractions that have the sequence M_z, the sequence of the multiplication by the coordinate functions on the vector-valued Hardy space H^2_ E(𝔻_2^(∞)) over the Hilbert's multidisk 𝔻_2^(∞), as their minimal isometric dilation for some Hilbert space ℰ. In this article, we remove the hypothesis of doubly commutativity and characterize all sequences of commuting contractions that are unitarily equivalent to (P_𝒬M_z_i|_𝒬)_i≥ 1 for some quotient module 𝒬 of H^2_ E(𝔻_2^(∞)). We further characterize those sequences for which 𝒬 is a Beurling quotient module. This generalizes Theorem 3.2 from \cite{BKD} to a sequence of commuting contractions.
ER  -