Extension of multilinear forms and polynomials from subspaces of L1-spaces

• Autores: Andreas Defant , Domingo García Rodríguez , Manuel Maestre Vera , David Pérez García
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 3, 2007, págs. 839-860
• Idioma: inglés
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• Resumen

  • Let X be a Banach space which has an unconditional basis and is a subspace of some L1-space Y. We show that X=l1 if and only if every m-linear form S on X, has an m-linear extension T to Y satisfying that ||T|| is less than or equal to Cm ||S||, where C > 0 is a constant independent of m. If we replace m-linear forms by m-homogeneous polynomials, then we can only show that X is "close'' to l1.