Propagation Phenomena for Operator-Valued Weighted Shifts

Raul E Curto; Abderrazzak Ech-charyfy; Hamza El Azhar; El Hassan Zerouali

doi:10.48550/arxiv.2604.05370

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Propagation Phenomena for Operator-Valued Weighted Shifts

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Propagation Phenomena for Operator-Valued Weighted Shifts

Raul E Curto, Abderrazzak Ech-charyfy, Hamza El Azhar and El Hassan Zerouali

ArXiv.org

Cornell University

04/07/2026

DOI: 10.48550/arxiv.2604.05370

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Abstract

This paper is devoted to the study of propagation phenomena for 2–hyponormal, quadratically hyponormal, and cubically hyponormal operator-valued weighted shifts. First, we show that every quadratically hyponormal matrix-valued weighted shift with two equal weights (excluding the initial weight) is flat. Second, we show that a cubically hyponormal operator-valued weighted shift with two equal weights (possibly including the initial weight) is flat. Next, we introduce a local flatness notion for matrix-valued weighted shifts. We prove that 2–hyponormal (in particular, subnormal) matrix-valued weighted shifts satisfy this stronger propagation phenomenon. As a result, we prove a structural decomposition theorem for 2–hyponormal matrix-valued weighted shifts.

Mathematics - Functional Analysis

Details

Title: Subtitle: Propagation Phenomena for Operator-Valued Weighted Shifts
Creators: Raul E Curto
Abderrazzak Ech-charyfy
Hamza El Azhar
El Hassan Zerouali
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2604.05370
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 04/07/2026
Academic Unit: Mathematics
Record Identifier: 9985151593302771

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