منابع مشابه
Weakly Compact Approximation in Banach Spaces
The Banach space E has the weakly compact approximation property (W.A.P. for short) if there is a constant C < ∞ so that for any weakly compact set D ⊂ E and ε > 0 there is a weakly compact operator V : E → E satisfying supx∈D ‖x − V x‖ < ε and ‖V ‖ ≤ C. We give several examples of Banach spaces both with and without this approximation property. Our main results demonstrate that the James-type ...
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Let (G,H) be a spherical pair and assume that G is a connected compact simple Lie group and H a closed subgroup of G. We prove in this paper that the homogeneous manifold G/H is weakly symmetric with respect to G and possibly an additional fixed isometry μ. It follows that M. Krämer’s classification list of such spherical pairs also becomes a classification list of compact weakly symmetric spac...
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Introduction. The two sections of this note are independent, but they are related by the fact that both use the results of [5 ] to obtain information on the properties of weakly compact sets in Banach spaces. In the first section we prove some results on a class of compact sets which is believed to include all weakly compact subsets of Banach spaces. We are interested in the properties of the n...
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The Banach space E has the weakly compact approximation property (W.A.P.) if there is C < ∞ so that the identity map IE can be uniformly approximated on any weakly compact subset D ⊂ E by weakly compact operators V on E satisfying ‖V ‖ ≤ C. We show that the spaces N(`, `) of nuclear operators ` → ` have the W.A.P. for 1 < q ≤ p < ∞, but that the Hardy space H does not have the W.A.P.
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ژورنال
عنوان ژورنال: Demonstratio Mathematica
سال: 2012
ISSN: 2391-4661
DOI: 10.1515/dema-2013-0411