Abstract
Let X and Y be Banach spaces. Then Kw*(X*, Y) denotes the Banach space of compact and weak*-weakly continuous linear operators from X* into Y, endowed with the usual operator norm. Let us write E⊃l∞ to indicate that a Banach space E contains an isomorphic copy of l∞. The purpose of this note is to prove the followingTheorem. Kw*(X*, Y) ⊃ l∞if and only if either X ⊃ l∞or Y ⊃ l∞.
Publisher
Cambridge University Press (CUP)
Reference7 articles.
1. Structural properties of operator spaces;Ruess;Acta Univ. Carolin. Math. Phys.,1987
2. Un théorème sur les opérateurs de l∞(Γ);Drewnowski;C.R. Acad. Sci. Paris Sér. A,1976
3. Vector Measures
4. On relatively disjoint families of measures, with some applications to Banach space theory
5. [6] Ruess W. . Duality and geometry of spaces of compact operators. In Functional Analysis: Surveys and Recent Results HI. Proc. 3rd Paderborn Conference 1983, North-Holland Math. Studies no. 90 (1984), pp. 59–78.
Cited by
19 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献