✦ LIBER ✦
On Ideals of Compact Operators Satisfying theM(r, s)-Inequality
✍ Scribed by Juan Carlos Cabello; Eduardo Nieto; Eve Oja
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 205 KB
- Volume
- 220
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
✦ Synopsis
Let r, s g 0, 1 . We prove that a Banach space X satisfies the M r, s -inequality Ži.e., 5 5 5 5 5 5 x*** G r x*** q s x*** y x*** ᭙ x*** g X ***, . where is the canonical projection of X *** onto X * whenever r q sr2 ) 1 and Ž . Ž . H there exists a norm one projection P on L L X * with Ker P s K K X satisfying
Ž .
Ž . Ž . We characterize the last property of K K X in L L X by a strong version of the metric compact approximation property of X. Our results extend some well-known results on M-ideals.