scholarly journals The Complete Continuity Property in Banach Spaces

2006 ◽  
Vol 36 (5) ◽  
pp. 1427-1435 ◽  
Author(s):  
Shangquan Bu ◽  
Eero Saksman
Keyword(s):  
Banach Spaces ◽  
Continuity Property ◽  
Complete Continuity

A Dual characterization of Banach Spaces With the Convex Point-of-Continuity Property

1989 ◽  
Vol 32 (3) ◽  
pp. 274-280
Author(s):  
D. E. G. Hare
Keyword(s):  
Banach Spaces ◽  
Continuity Property ◽  
Dual Spaces ◽  
Equivalent Norms ◽  
Fréchet Differentiability ◽  
New Type ◽  
Frechet Differentiability ◽  
Point Of Continuity Property ◽  
Convex Point

AbstractWe introduce a new type of differentiability, called cofinite Fréchet differentiability. We show that the convex point-of-continuity property of Banach spaces is dual to the cofinite Fréchet differentiability of all equivalent norms. A corresponding result for dual spaces with the weak* convex point-of-continuity property is also established.

scholarly journals Some properties of the projective tensor product UX derived from those of U and X

2006 ◽  
Vol 73 (1) ◽  
pp. 37-45 ◽  
Author(s):  
Patrick N. Dowling
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Unconditional Basis ◽  
Complex Banach Space ◽  
Continuity Property ◽  
Complete Continuity ◽  
Projective Tensor Product ◽  
Projective Tensor

Let X be a real or complex Banach space and let U be a Banach space with an unconditional basis. We show that the projective tensor product of U and X, UX, has the complete continuity property (respectively, the analytic complete continuity property) whenever U and X have the complete continuity property (respectively, the analytic complete continuity property). More general versions of these results are also obtained. Moreover, the techniques applied here to the projective tensor product, can also be used to establish some Banach space properties of the Fremlin projective tensor product.

scholarly journals The Complete Continuity Property and Finite Dimensional Decompositions

1995 ◽  
Vol 38 (2) ◽  
pp. 207-214
Author(s):  
Maria Girardi ◽  
William B. Johnson
Keyword(s):  
Banach Space ◽  
Local Structure ◽  
Continuity Property ◽  
Complete Continuity ◽  
Bounded Linear ◽  
Completely Continuous ◽  
Finite Dimensional ◽  
Dimensional Decomposition ◽  
Finite Dimensional Decomposition ◽  
Convergent Sequences

AbstractA Banach space has the complete continuity property (CCP) if each bounded linear operator from L1 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.

Sign in / Sign up

Export Citation Format

Share Document