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April 2009 Slices in the unit ball of the symmetric tensor product of $\mathcal{C}(K)$ and L1(μ)
María D. Acosta, Julio Becerra Guerrero
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Ark. Mat. 47(1): 1-12 (April 2009). DOI: 10.1007/s11512-007-0057-6


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.


Dedicated to Angel Rodríguez Palacios on the occasion of his 60th birthday.


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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.


Received: 2 March 2007; Published: April 2009
First available in Project Euclid: 31 January 2017

zbMATH: 1183.46007
MathSciNet: MR2480913
Digital Object Identifier: 10.1007/s11512-007-0057-6

Rights: 2008 © Institut Mittag-Leffler


Vol.47 • No. 1 • April 2009
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