Banach spaces with polynomial numerical index 1
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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We characterize Banach spaces with polynomial numerical index 1 when they have the Radon-Nikod´ym property. The holomorphic numerical index is introduced and the characterization of the Banach space with holomorphic numerical index 1 is obtained when it has the Radon-Nikod´ym property.
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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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The classical Stone-Weierstrass theorem claims that the algebra of all real polynomials on a finite-dimensional real Banach space X is dense, in the topology of uniform convergence on bounded sets (we will always consider this topology, unless otherwise stated), in the space of continuous real functions on X. On the other hand ([12]), on every infinite-dimensional Banach space X there exists a ...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2008
ISSN: 0024-6093
DOI: 10.1112/blms/bdm113