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
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.
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
@article{10_4153_CMB_1995_029_6,
author = {Girardi, Maria and Johnson, William B.},
title = {The {Complete} {Continuity} {Property} and {Finite} {Dimensional} {Decompositions}},
journal = {Canadian mathematical bulletin},
pages = {207--214},
year = {1995},
volume = {38},
number = {2},
doi = {10.4153/CMB-1995-029-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-029-6/}
}
TY - JOUR AU - Girardi, Maria AU - Johnson, William B. TI - The Complete Continuity Property and Finite Dimensional Decompositions JO - Canadian mathematical bulletin PY - 1995 SP - 207 EP - 214 VL - 38 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-029-6/ DO - 10.4153/CMB-1995-029-6 ID - 10_4153_CMB_1995_029_6 ER -
%0 Journal Article %A Girardi, Maria %A Johnson, William B. %T The Complete Continuity Property and Finite Dimensional Decompositions %J Canadian mathematical bulletin %D 1995 %P 207-214 %V 38 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-029-6/ %R 10.4153/CMB-1995-029-6 %F 10_4153_CMB_1995_029_6
Cité par Sources :