Affiliation:
1. University of Wisconsin-River Falls Department of Mathematics River Falls, WI 54022-5001 USA
Abstract
Abstract
We characterize Banach spaces X with spaces with property (wL), i.e. spaces with the property that every L-subset of X* is weakly precompact. We prove that a Banach space X has property (wL) if and only if for any Banach space Y, any completely continuous operator T : X → Y has weakly precompact adjoint if and only if any completely continuous operator T : X → ℓ
∞ has weakly precompact adjoint.
We prove that if E is a Banach space and F is a reflexive subspace of E* such that ⊥
F has property (wL), then E has property (wL). We show that a space E has property RDP* (resp. the DPrcP) if and only if any closed separable subspace of E has property RDP* (resp. the DPrcP). We also show that G has property (wL) if under some conditions K
w*
(E*, F) contains the dual of G.
Reference32 articles.
1. Alihommady, M.: Weak convergence in spaces of measures and operators, Bull. Belg. Math. Soc. 6 (1999), 465–471.
2. Andrews, K.: Dunford-Pettis sets in the space of Bochner integrable functions, Math. Ann. 241 (1979), 35–41.
3. Bator, E. M.: Remarks on completely continuous operators, Bull. Polish Acad. Sci. Math. 37 (1989), 409–413.
4. Bator, E.—Lewis, P.: Properties (V) and (wV) on C(Ω,X), Math. Proc. Camb. Phil. Soc 117 (1995), 469–477.
5. Bator, E.—Lewis, P.: Operators having weakly precompact addoints, Math. Nachr. 157 (1992), 99–103.
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