Propagation Phenomena for Operator-Valued Weighted Shifts
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910202346864640 |
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| author | Curto, Raul E. Ech-charyfy, Abderrazzak Azhar, Hamza El Zerouali, El Hassan |
| author_facet | Curto, Raul E. Ech-charyfy, Abderrazzak Azhar, Hamza El Zerouali, El Hassan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05370 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Propagation Phenomena for Operator-Valued Weighted Shifts Curto, Raul E. Ech-charyfy, Abderrazzak Azhar, Hamza El Zerouali, El Hassan Functional Analysis 47B20, 47B37, 47A08 (Primary) 47A57 (Secondary) 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. |
| title | Propagation Phenomena for Operator-Valued Weighted Shifts |
| topic | Functional Analysis 47B20, 47B37, 47A08 (Primary) 47A57 (Secondary) |
| url | https://arxiv.org/abs/2604.05370 |