Let X be a Banach space and Β΅ be a finite measure space. It is shown that if 1 β€ p < β resp 1 < p < β , the Bochner space L p Β΅ X contains asymptotically isometric copies of c 0 resp l 1 if and only if X does.
Complemented Copies of l1 in Orlicz Spaces
β Scribed by Shutao Chen; Henryk Hudzik; Huying Sun
- Publisher
- John Wiley and Sons
- Year
- 1992
- Tongue
- English
- Weight
- 468 KB
- Volume
- 159
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let X be a Banach space. Let ?i,.(X\*) the M e t space whose elements are the holomorphic functions defined on X\* whose restrictions to each multiple mB(X\*), m = 1,2, . . . , of the closed unit ball B ( X \* ) of X\* are continuous for the weak-star topology. A fundamental Hystem of norms for this
## Abstract We introduce the notions of __X__~d,s(x),Ο~βlinear multifunctional and __X__~d,s(x),Ο~βlinear continuous multifunctional. We generalize the theorems on linear bounded functionals in the MusielakβOrlicz space.
An extension of the Marcinkiewicz interpolation theorem is proved, yielding a necessary and sufficient condition for every quasilinear operator, satisfying given endpoint estimates of weak type, to be bounded from an Orlicz space into another. 1998 Academic Press in the last three papers mentioned