Geodesic
Polynomial Grothendieck properties
Glasgow mathematical journal, Tome 37 (1995) no. 2, pp. 211-219

Voir la notice de l'article provenant de la source Cambridge University Press

A Banach space sE has the Grothendieck property if every (linear bounded) operator from E into c0 is weakly compact. It is proved that, for an integer k > 1, every k-homogeneous polynomial from E into c0 is weakly compact if and only if the space (kE) of scalar valued polynomials on E is reflexive. This is equivalent to the symmetric A>fold projective tensor product of £(i.e., the predual of (kE)) having the Grothendieck property. The Grothendieck property of the projective tensor product EF is also characterized. Moreover, the Grothendieck property of E is described in terms of sequences of polynomials. Finally, it is shown that if every operator from E into c0 is completely continuous, then so is every polynomial between these spaces. 
González, Manuel; Gutiérrez, Joaquí M. Polynomial Grothendieck properties. Glasgow mathematical journal, Tome 37 (1995) no. 2, pp. 211-219. doi: 10.1017/S0017089500031116
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