Illinois Journal of Mathematics

Descriptive theory of nearest points in Banach spaces

Robert Kaufman

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Let $X$ be a separable Banach space, $Y$ a closed, nonreflexive, linear subspace, and $P$ the set of points admitting a nearest approximation in $Y$. Then $P$ is an analytic set, and has three obvious algebraic properties. By adjusting the norm of $X$, any analytic set of this kind can be realized as the set of elements proximal to $Y$.

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Illinois J. Math., Volume 54, Number 3 (2010), 1157-1162.

First available in Project Euclid: 3 May 2012

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Primary: 46B20: Geometry and structure of normed linear spaces 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
Secondary: 46B03: Isomorphic theory (including renorming) of Banach spaces


Kaufman, Robert. Descriptive theory of nearest points in Banach spaces. Illinois J. Math. 54 (2010), no. 3, 1157--1162. doi:10.1215/ijm/1336049988.

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