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arXiv · 2604.05370

Propagation Phenomena for Operator-Valued Weighted Shifts

Raul E. Curto·Abderrazzak Ech-charyfy·Hamza El Azhar·El Hassan Zerouali
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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 {\it quadratically} hyponormal matrix-valued weighted shift with two equal weights ({\it excluding the initial weight}) is flat. \ Second, we show that a {\it cubically} hyponormal operator-valued weighted shift with two equal weights ({\it possibly including the initial weight}) is flat. \ Next, we introduce a {\it 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 {\it structural decomposition theorem} for $2$--hyponormal matrix-valued weighted shifts.

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BibTeXRIS

Raul E. Curto, Abderrazzak Ech-charyfy, Hamza El Azhar, El Hassan Zerouali. 2026-04-07. Propagation Phenomena for Operator-Valued Weighted Shifts. https://doi.org/10.1007/s00025-025-02572-6

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