On the spectrum of the symmetric tensor products of certain Hilbert-space operators
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908527100952576 |
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| author | Yang, Yuchi Zhang, Yuanhang |
| author_facet | Yang, Yuchi Zhang, Yuanhang |
| contents | This paper primarily investigates spectral properties of symmetric tensor products of Hilbert-space operators. For a unilateral weighted shift operator $S_w$, we present an algorithm to compute the point spectrum of its symmetric and antisymmetric tensor products with the adjoint $S_w^*$. Additionally, we analyze the symmetric tensor product of an injective unilateral weighted shift $S_α$ and a diagonal operator $M$ on $l^2$, demonstrating that its point spectrum must be contained in $\{0\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the spectrum of the symmetric tensor products of certain Hilbert-space operators Yang, Yuchi Zhang, Yuanhang Functional Analysis 46B28, 47A10 This paper primarily investigates spectral properties of symmetric tensor products of Hilbert-space operators. For a unilateral weighted shift operator $S_w$, we present an algorithm to compute the point spectrum of its symmetric and antisymmetric tensor products with the adjoint $S_w^*$. Additionally, we analyze the symmetric tensor product of an injective unilateral weighted shift $S_α$ and a diagonal operator $M$ on $l^2$, demonstrating that its point spectrum must be contained in $\{0\}$. |
| title | On the spectrum of the symmetric tensor products of certain Hilbert-space operators |
| topic | Functional Analysis 46B28, 47A10 |
| url | https://arxiv.org/abs/2509.07374 |