منابع مشابه
Q-reflexive Banach Spaces
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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We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the MilmanPettis theorem that uniformly convex Banach spaces are reflexive. Our aim in this note is to present a fully constructive analysis of the Milman-Pettis theorem [11, 12, 9, 13]: a uniformly convex Banach space is reflexive. First, t...
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Let $X$ be a Banach space, $Csubset X$ be a closed convex set included in a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set $C$, so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...
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A convex set C ⊆ X∗∗ × X∗ admits the variant Banach-Dieudonné property (VBDP) if the weak∗-strong closure C w×‖·‖ is the smallest set containing C that is closed to all limits of its bounded and weak∗×‖ · ‖ convergent nets. We show in particular, that all convex sets in X∗∗×X∗ admit the VBDP when E∗ := X∗×X∗∗ is weakly-compactly generated (WCG) and hence if E is either a dual separable or a ref...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1970
ISSN: 1385-7258
DOI: 10.1016/s1385-7258(70)80039-7