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