Norm-preserving extensions of functionals and denting points of convex sets期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Norm-preserving extensions of functionals and denting points of convex sets

Authors:	Eve Oja Märt Põldvere

Institution:	(1) Institute of Pure Mathematics, University of Tartu, J. Liivi 2, 50409 Tartu, Estonia

Abstract:	Let W and Z be Banach spaces, and let $X\subset W$ and $Y\subset Z$ be closed subspaces. Let $\mathcal{L}$ be a subspace of $\mathcal{L}(W^, Z^{})$ , the Banach space of bounded linear operators from W to Z*, containing $X\otimes Y$ . We describe, for $x^{}\in X^{}$ and $y^\in Y^$ , all norm-preserving extensions of $x^{}\otimes y^{*}\in (X\otimes Y)^\ast$ to the space $\mathcal{L}$ in terms of convergence of convex combinations. We also characterize denting points of bounded convex subsets of Banach spaces in similar terms. Various applications are presented. Supported by Estonian Science Foundation Grant 5704.

Keywords:	Norm-preserving extensions of functionals Spaces of operators Denting points Ideals in Banach spaces
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