finite dimensional decomposition
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2019 ◽  
Vol 71 (1) ◽  
pp. 139-174
Author(s):  
Jesús M F Castillo ◽  
Yolanda Moreno

Abstract We introduce and study the notion of space of almost universal complemented disposition (a.u.c.d.) as a generalization of Kadec space. We show that every Banach space with separable dual is isometrically contained as a $1$-complemented subspace of a separable a.u.c.d. space and that all a.u.c.d. spaces with $1$-finite dimensional decomposition (FDD) are isometric and contain isometric $1$-complemented copies of every separable Banach space with $1$-FDD. We then study spaces of universal complemented disposition (u.c.d.) and provide different constructions for such spaces. We also consider spaces of u.c.d. with respect to separable spaces.





1995 ◽  
Vol 38 (2) ◽  
pp. 207-214
Author(s):  
Maria Girardi ◽  
William B. Johnson

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.





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