Abstract and Applied Analysis

On projection constant problems and the existence of metric projections in normed spaces

Entisarat El-Shobaky, Sahar Mohammed Ali, and Wataru Takahashi

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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 lp,1p< and c0. We also give the sufficient and necessary conditions for an infinite matrix to represent a projection operator from lp,1p< or c0 onto anyone of their maximal proper subspaces.

Article information

Abstr. Appl. Anal., Volume 6, Number 7 (2001), 401-411.

First available in Project Euclid: 13 April 2003

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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

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