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
Metric projections after renorming
✍ Scribed by Libor Veselý
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 522 KB
- Volume
- 66
- Category
- Article
- ISSN
- 0021-9045
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📜 SIMILAR VOLUMES
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 |2Â p&1| , for every subspace M of L
The paper is concerned with the calculation of the derived mapping of the metric projection onto a finite dimensional subspace of a space of integrable functions. Abstract results for quotient spaces and for spaces which are \(l^{\prime}\)-direct sums are obtained and are applied to real or complex