Extremal Schur Multipliers
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917818504577024 |
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| author | Christensen, Erik |
| author_facet | Christensen, Erik |
| contents | The Schur product of two complex m x n matrices is their entry wise product. We show that an extremal element X in the convex set of m x n complex matrices of Schur multiplier norm at most 1 satisfies the inequality rank(X) =< (m +n)^(1/2) . For positive n x n matrices with unit diagonal, we give a characterization of the extremal elements, and show that such a matrix satisfies rank(X) =< n^(1/2). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20112 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extremal Schur Multipliers Christensen, Erik Functional Analysis Mathematical Physics Quantum Algebra 15A23, 52A21, 81P47 (Primary) 15A60, 46L07 (Secondary) The Schur product of two complex m x n matrices is their entry wise product. We show that an extremal element X in the convex set of m x n complex matrices of Schur multiplier norm at most 1 satisfies the inequality rank(X) =< (m +n)^(1/2) . For positive n x n matrices with unit diagonal, we give a characterization of the extremal elements, and show that such a matrix satisfies rank(X) =< n^(1/2). |
| title | Extremal Schur Multipliers |
| topic | Functional Analysis Mathematical Physics Quantum Algebra 15A23, 52A21, 81P47 (Primary) 15A60, 46L07 (Secondary) |
| url | https://arxiv.org/abs/2410.20112 |