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Slices in the unit ball of the symmetric tensor product of $\mathcal{C}(K)$ and$L$_{1}(μ)

María D. Acosta Departamento de Análisis Matemático, Universidad de Granada Julio Becerra Guerrero Departamento de Matemática Aplicada, Universidad de Granada

TBD mathscidoc:1701.333137

Arkiv for Matematik, 47, (1), 1-12, 2007.3
We prove that for the cases $X=\mathcal{C}(K)$ ($K$infinite) and$X$=$L$_{1}(μ) (μ σ-finite and atomless) it holds that every slice of the unit ball of the$N$-fold symmetric tensor product of$X$has diameter two. In fact, we prove more general results for weak neighborhoods relative to the unit ball. As a consequence, we deduce that the spaces of$N$-homogeneous polynomials on those classical Banach spaces have no points of Fréchet differentiability.
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@inproceedings{maría2007slices,
  title={Slices in the unit ball of the symmetric tensor product of $\mathcal{C}(K)$ and$L$_{1}(μ)},
  author={María D. Acosta, and Julio Becerra Guerrero},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203623666861946},
  booktitle={Arkiv for Matematik},
  volume={47},
  number={1},
  pages={1-12},
  year={2007},
}
María D. Acosta, and Julio Becerra Guerrero. Slices in the unit ball of the symmetric tensor product of $\mathcal{C}(K)$ and$L$_{1}(μ). 2007. Vol. 47. In Arkiv for Matematik. pp.1-12. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203623666861946.
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