Model Theory for Operators Related to Square Roots of Normal Operators

Raul E Curto; Thankarajan Prasad

doi:10.48550/arxiv.2607.21450

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Model Theory for Operators Related to Square Roots of Normal Operators

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Model Theory for Operators Related to Square Roots of Normal Operators

Raul E Curto and Thankarajan Prasad

arXiv (Cornell University)

arXiv

07/23/2026

DOI: 10.48550/arxiv.2607.21450

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Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

In this paper we prove that a square root of a cyclic normal operator is unitarily equivalent to a block multiplication operator on a vector-valued Lebesgue space with a2 –normal symbol. In addition, we show that a cyclic operator which admits a cyclic2 –normal extension is unitarily equivalent to a block multiplication operator on a corresponding vector-valued Hardy space with2 –normal symbol. We consider the existence of bounded point evaluations in the vector-valued Hardy space setting; as an application, we prove that an operator admitting a cyclic2 –normal extension has nontrivial invariant subspaces. We also study uniqueness for minimaln –normal extensions of operators that have cyclic2 –normal extensions.

Mathematics - Functional Analysis

Details

Title: Subtitle: Model Theory for Operators Related to Square Roots of Normal Operators
Creators: Raul E Curto
Thankarajan Prasad
Resource Type: Preprint
Publication Details: arXiv (Cornell University)
DOI: 10.48550/arxiv.2607.21450
ISSN: 2331-8422
Publisher: arXiv
Language: English
Date posted: 07/23/2026
Academic Unit: Mathematics
Record Identifier: 9985183559302771

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