Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 6, Number 7 (2001), 401-411.
On projection constant problems and the existence of metric projections in normed spaces
We give the sufficient conditions for the existence of a metric projection onto convex closed subsets of normed linear spaces which are reduced conditions than that in the case of reflexive Banach spaces and we find a general formula for the projections onto the maximal proper subspaces of the classical Banach spaces and . We also give the sufficient and necessary conditions for an infinite matrix to represent a projection operator from or onto anyone of their maximal proper subspaces.
Abstr. Appl. Anal., Volume 6, Number 7 (2001), 401-411.
First available in Project Euclid: 13 April 2003
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 41A50: Best approximation, Chebyshev systems 41A52: Uniqueness of best approximation
Secondary: 46A32: Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20] 46N10: Applications in optimization, convex analysis, mathematical programming, economics
El-Shobaky, Entisarat; Ali, Sahar Mohammed; Takahashi, Wataru. On projection constant problems and the existence of metric projections in normed spaces. Abstr. Appl. Anal. 6 (2001), no. 7, 401--411. doi:10.1155/S1085337501000732. https://projecteuclid.org/euclid.aaa/1050266950