𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the norms of metric projections

✍ Scribed by Mark A Smith


Book ID
107776780
Publisher
Elsevier Science
Year
1981
Tongue
English
Weight
342 KB
Volume
31
Category
Article
ISSN
0021-9045

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


On the Norm of the Metric Projections
✍ Fernando Mazzone πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 87 KB

Let X be a Banach space. Given M a subspace of X we denote with P M the metric projection onto M. We define ?(X ) :=sup [&P M &: M a proximinal subspace of X]. In this paper we give a bound for ?(X ). In particular, when X=L p , we obtain the inequality &P M & 2 |2Γ‚ p&1| , for every subspace M of L

On continuity of metric projections
✍ Frank Deutsch; Joseph M Lambert πŸ“‚ Article πŸ“… 1980 πŸ› Elsevier Science 🌐 English βš– 851 KB
A Note on Metric Projections
✍ F. Mazzone; H. Cuenya πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 147 KB

In this note we give an example of a strictly convex, reflexive, smooth Banach space which has a Chebyshev subspace \(M\), such that the projection onto \(M\) is linear and has norm equal to 2 . Moreover, we give necessary and sufficient conditions on a space so that every projection has norm less t

Norms of Minimal Projections
✍ H. Konig; N. Tomczakjaegermann πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 862 KB

It is proved that the projection constants of two- and three-dimensional spaces are bounded by \(\frac{4}{3}\) and \((1+\sqrt{5}) / 2\), respectively. These bounds are attained precisely by the spaces whose unit balls are the regular hexagon and dodecahedron. In fact, a general inequality for the pr