Journal of Operator Theory

Volume 92, Issue 1, Summer 2024 pp. 257-281.

Orthogonal decompositions and twisted isometries. II

Authors: Narayan Rakshit (1), Jaydeb Sarkar (2), Mansi Suryawanshi (3)
Author institution:(1) Indian Institute of Technology, Roorkee- 247667, Uttarakhand, India
(2) Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, Bangalore, 560059, India
(3) Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, Bangalore, Karnataka - 560059, India

Summary: 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.

DOI: http://dx.doi.org/10.7900/jot.2022oct05.2415
Keywords: isometries, von Neumann and Wold decompositions, shift operators, wandering subspaces, invariant subspaces, Hardy space, polydisc

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