scholarly journals A Note on the Analytic Complete Continuity Property

2002 ◽  
Vol 265 (2) ◽  
pp. 463-467 ◽  
Author(s):  
Shangquan Bu
Keyword(s):  
Continuity Property ◽  
Complete Continuity

scholarly journals The complete continuity property in Bochner function spaces

1993 ◽  
Vol 117 (4) ◽  
pp. 1109-1109 ◽  
Author(s):  
Narcisse Randrianantoanina ◽  
Elias Saab
Keyword(s):  
Function Spaces ◽  
Continuity Property ◽  
Complete Continuity

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 in Banach Spaces

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

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.

scholarly journals The Analytic Complete Continuity Property

2000 ◽  
Vol 252 (2) ◽  
pp. 967-979 ◽  
Author(s):  
Mangatiana A. Robdera ◽  
Paulette Saab
Keyword(s):  
Continuity Property ◽  
Complete Continuity

scholarly journals Semi-continuity for total dimension divisors of étale sheaves

2017 ◽  
Vol 28 (01) ◽  
pp. 1750001
Author(s):  
Haoyu Hu ◽  
Enlin Yang
Keyword(s):  
Continuity Property ◽  
Lower Semi ◽  
Total Dimension

In this paper, we extend an inequality that compares the pull-back of the total dimension divisor of an étale sheaf and the total dimension divisor of the pull-back of the sheaf due to Saito. Using this formula, we generalize Deligne and Laumon’s lower semi-continuity property for Swan conductors of étale sheaves on relative curves to higher relative dimensions in a geometric situation.

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