Numerical index of Banach spaces and duality
نویسندگان
چکیده
منابع مشابه
Real Banach Spaces with Numerical Index 1
We show that an infinite-dimensional real Banach space with numerical index 1 satisfying the Radon– Nikodỳm property contains l1. It follows that a reflexive or quasi-reflexive real Banach space cannot be re-normed to have numerical index 1, unless it is finite-dimensional.
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Let X be a Banach space with the Radon-Nikodỳm property. Then, the following are equivalent. (i) X has numerical index 1. (ii) |x∗∗(x∗)| = 1 for all x∗ ∈ ex(BX∗ ) and x∗∗ ∈ ex(BX∗∗ ). (iii) X is an almost-CL-space. (iv) There are a compact Hausdorff space K and a linear isometry J : X → C(K) such that |x∗∗(J∗δs)| = 1 for all s ∈ K and x∗∗ ∈ ex(BX∗∗ ). If X is a real space, the above conditions ...
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2007
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004106009650