Abstract
We prove that for the cases $X=\mathcal{C}(K)$ (K infinite) and X=L1(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.
Dedication
Dedicated to Angel Rodríguez Palacios on the occasion of his 60th birthday.
Citation
María D. Acosta. Julio Becerra Guerrero. "Slices in the unit ball of the symmetric tensor product of $\mathcal{C}(K)$ and L1(μ)." Ark. Mat. 47 (1) 1 - 12, April 2009. https://doi.org/10.1007/s11512-007-0057-6
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