Column bounded matrices and Grothendieck's inequalities
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912365899939840 |
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| author | Christensen, Erik |
| author_facet | Christensen, Erik |
| contents | It follows from Grothendieck's little inequality that to any complex (m x n) matrix X of column norm at most 1, and an 0 <e <1, there exist a natural number q, an (m x q) matrix C with
$(1-e)^2 \leq CC^* \leq (4/π) (1 + e)^2$
and an (q x n ) matrix Z with entries in the complex torus such that X= q$^{-(1/2)}$(CZ). Both of Grothendieck's complex inequalities follow from this factorization result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Column bounded matrices and Grothendieck's inequalities Christensen, Erik Functional Analysis Mathematical Physics Operator Algebras Quantum Algebra 15A23, 15A60, 46B25, 47L25, 52A21, 81P40 It follows from Grothendieck's little inequality that to any complex (m x n) matrix X of column norm at most 1, and an 0 <e <1, there exist a natural number q, an (m x q) matrix C with $(1-e)^2 \leq CC^* \leq (4/π) (1 + e)^2$ and an (q x n ) matrix Z with entries in the complex torus such that X= q$^{-(1/2)}$(CZ). Both of Grothendieck's complex inequalities follow from this factorization result. |
| title | Column bounded matrices and Grothendieck's inequalities |
| topic | Functional Analysis Mathematical Physics Operator Algebras Quantum Algebra 15A23, 15A60, 46B25, 47L25, 52A21, 81P40 |
| url | https://arxiv.org/abs/2505.04545 |