Propagation Phenomena for Operator-Valued Weighted Shifts
Raúl Curto, Abderrazzak Ech-charyfy, Hamza El Azhar, El Hassan Zerouali
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Source: Crossref
Published: Dec 13, 2025
DOI: 10.1007/s00025-025-02572-6
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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.
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