论文信息 - A uniformly convex Banach space which contains no cp

A uniformly convex Banach space which contains no cp

There is a uniformly convex Banach space with unconditional basis which contains no subspace isomorphic to any lp (1 p ~). The space may be chosen either to have a symmetric basis, or so that it contains no subsymmetric basic sequence. It is proved that a super-reflexive space with local unconditional structure can be equivalently normed so that its modulus of convexity is of power type.

W. B. Johnson | T. Figiel | W. Johnson | T. Figiel

[1] W. Johnson. On finite dimensional subspaces of Banach spaces with local unconditional structure , 1974 .

[2] Per Enflo,et al. Banach spaces which can be given an equivalent uniformly convex norm , 1972 .

[3] T. Figiel. An example of infinite dimensional reflexive Banach space non-isomorphic to its Cartesian square , 1972 .