English

S{\l}oci\'nski-Wold decompositions for row-isometries

Functional Analysis 2022-03-15 v2 Operator Algebras

Abstract

S{\l}oci\'nski gave sufficient conditions for commuting isometries to have a nice Wold-like decomposition. In this note we provide analogous results for row-isometries satisfying certain commutation relations. Other than known results for doubly-commuting row-isometries, we provide sufficient condtions for a Wold decomposition based on the Lebesgue decomposition of the row-isometries.

Keywords

Cite

@article{arxiv.2203.03504,
  title  = {S{\l}oci\'nski-Wold decompositions for row-isometries},
  author = {Adam H. Fuller},
  journal= {arXiv preprint arXiv:2203.03504},
  year   = {2022}
}

Comments

10 pages; added proof that operators commuting with a row-isometry are reduced by the singular part of the row-isometry