## Illinois Journal of Mathematics

### Descriptive theory of nearest points in Banach spaces

Robert Kaufman

#### Abstract

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 $Y$.

#### Article information

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

Dates
First available in Project Euclid: 3 May 2012

https://projecteuclid.org/euclid.ijm/1336049988

Digital Object Identifier
doi:10.1215/ijm/1336049988

Mathematical Reviews number (MathSciNet)
MR2928349

Zentralblatt MATH identifier
1264.46009

#### Citation

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

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