Few Bilinear Operators on Spaces of Continuous Functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912632477319168 |
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| author | Candido, Leandro |
| author_facet | Candido, Leandro |
| contents | Motivated by recent work exhibiting a locally compact scattered space $L$ constructed under Ostaszewski's $\clubsuit$-principle, which yielded a complete classification of linear operators on $C_0(L\times L)$, we extend the analysis to the bilinear setting. We show that, for this space $L$, every bilinear operator $G:C_0(L)\times C_0(L)\to C_0(L)$ admits a unique decomposition into the sum of trivially predictable components. This establishes a bilinear analogue of the few operators phenomenon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05322 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Few Bilinear Operators on Spaces of Continuous Functions Candido, Leandro Functional Analysis Motivated by recent work exhibiting a locally compact scattered space $L$ constructed under Ostaszewski's $\clubsuit$-principle, which yielded a complete classification of linear operators on $C_0(L\times L)$, we extend the analysis to the bilinear setting. We show that, for this space $L$, every bilinear operator $G:C_0(L)\times C_0(L)\to C_0(L)$ admits a unique decomposition into the sum of trivially predictable components. This establishes a bilinear analogue of the few operators phenomenon. |
| title | Few Bilinear Operators on Spaces of Continuous Functions |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2510.05322 |