Slices in the unit ball of the symmetric tensor product of C(K)C(K) and L 1(µ)

• Autores: María Dolores Acosta Vigil , Julio Becerra Guerrero
• Localización: Arkiv för matematik, ISSN 0004-2080, Vol. 47, Nº 1, 2009, págs. 1-12
• Idioma: inglés
• DOI: 10.1007/s11512-007-0057-6
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• Resumen

  • We prove that for the cases X=C(K) (K infinite) and X=L1(m) (m s-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.