Słociński-Wold decompositions for row-isometries

Abstract

Słociński 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.

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