Geodesic
The Complete Continuity Property and Finite Dimensional Decompositions
Canadian mathematical bulletin, Tome 38 (1995) no. 2, pp. 207-214

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

A Banach space has the complete continuity property (CCP) if each bounded linear operator from L 1 into is completely continuous (i.e., maps weakly convergent sequences to norm convergent sequences). The main theorem shows that a Banach space failing the CCP has a subspace with a finite dimensional decomposition which fails the CCP. If furthermore the space has some nice local structure (such as fails cotype or is a lattice), then the decomposition may be strengthened to a basis.
DOI : 10.4153/CMB-1995-029-6
Mots-clés : 46B22, 46B20, 46B28, 46G99 
Girardi, Maria; Johnson, William B. The Complete Continuity Property and Finite Dimensional Decompositions. Canadian mathematical bulletin, Tome 38 (1995) no. 2, pp. 207-214. doi: 10.4153/CMB-1995-029-6
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