Weakly p-Compact, p-Banach-Saks, and Super-reflexive Banach Spaces
نویسندگان
چکیده
منابع مشابه
On Weakly Compact Subsets of Banach Spaces
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. 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 E be a Banach space. There are several natural ways in which any polynomial P ∈ P(E) can be extended to P̃ ∈ P(E), in such a way that the extension mapping is continuous and linear (see, for example, [6]). Taking the double transpose of the extension mapping P → P̃ yields a linear, continuous mapping from P(E) into P(E). Further, since P(E) is a dual space, it follows that there is a natural ...
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In this paper we first take a detail survey of the study of the Banach-Saks property of Banach spaces and then show the Banach-Saks property of the product spaces generated by a finite number of Banach spaces having the Banach-Saks property. A more general inequality for integrals of a class of composite functions is also given by using this property.
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Given p ≥ 1, we denote by Cp the class of all Banach spaces X satisfying the equality Kp(Y,X) = Πp(Y,X) for every Banach space Y , Kp (respectively, Πp) being the operator ideal of p-compact operators (respectively, of operators with p-summing adjoint). If X belongs to Cp, a bounded set A ⊂ X is relatively p-compact if and only if the evaluation map U∗ A : X ∗ −→ ∞(A) is p-summing. We obtain p-...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1994
ISSN: 0022-247X
DOI: 10.1006/jmaa.1994.1246