Orthogonal decompositions and twisted isometries II
Functional Analysis
2022-09-29 v1 Complex Variables
Operator Algebras
Abstract
We classify tuples of (not necessarily commuting) isometries that admit von Neumann-Wold decomposition. We introduce the notion of twisted isometries for tuples of isometries and prove the existence of orthogonal decomposition for such tuples. The former classification is partially inspired by a result that was observed more than three decades ago by Gaspar and Suciu. And the latter result generalizes Popovici's orthogonal decompositions for pairs of commuting isometries to general tuples of twisted isometries which also includes the case of tuples of commuting isometries. Our results unify all the known orthogonal decomposition related results in the literature.
Cite
@article{arxiv.2209.14014,
title = {Orthogonal decompositions and twisted isometries II},
author = {Narayan Rakshit and Jaydeb Sarkar and Mansi Suryawanshi},
journal= {arXiv preprint arXiv:2209.14014},
year = {2022}
}
Comments
24 pages. [See arXiv:2104.07628 for Part I]