Sharp lower bounds for generalized operator products
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911350290120704 |
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| author | Guillot, Dominique Mashreghi, Javad Vishwakarma, Prateek Kumar |
| author_facet | Guillot, Dominique Mashreghi, Javad Vishwakarma, Prateek Kumar |
| contents | We consider general bilinear products defined by positive semidefinite matrices. Typically non-commutative, non-associative, and non-unital, these products preserve positivity and include the classical Hadamard, Kronecker, and convolutional products as special cases. We prove that every such product satisfies a sharp nonzero lower bound in the Loewner order, generalizing previous results of Vybíral [Adv. Math., 2020] and Khare [Proc. Amer. Math. Soc., 2021] that were obtained in the special case of the Hadamard product. Our results naturally extend to Hilbert spaces for a family of products parametrized by positive trace-class operators, providing a lower bound in the Loewner order for such general products, including for the Hilbert tensor product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00409 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp lower bounds for generalized operator products Guillot, Dominique Mashreghi, Javad Vishwakarma, Prateek Kumar Functional Analysis We consider general bilinear products defined by positive semidefinite matrices. Typically non-commutative, non-associative, and non-unital, these products preserve positivity and include the classical Hadamard, Kronecker, and convolutional products as special cases. We prove that every such product satisfies a sharp nonzero lower bound in the Loewner order, generalizing previous results of Vybíral [Adv. Math., 2020] and Khare [Proc. Amer. Math. Soc., 2021] that were obtained in the special case of the Hadamard product. Our results naturally extend to Hilbert spaces for a family of products parametrized by positive trace-class operators, providing a lower bound in the Loewner order for such general products, including for the Hilbert tensor product. |
| title | Sharp lower bounds for generalized operator products |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2601.00409 |