We obtain a sucint and nesessery theoreoms simple for compactness and weakly compactness of the best approximate sets by closed unit balls. Also we consider relations Kadec-Klee property and shur property with this objects. These theorems are extend of papers mohebi and Narayana.
References
[1] F. Deutsch, Best approximation in inner product spaces., CMS Books in Mathematics/Ouvrages de Mathmatiques de la SMC, 7. Springer-Verlag, New York, 2001. [2] H. Mohebi, On quasi-Chebyshev subspaces of Banach spaces. J. Approx. Theory 107 (2000), no. 1, 87-95. [3] H. Mohebi, On quasi-Chebyshev subspaces of Banach spaces. J. Approx. Theory 107 (2000), no. 1, 87-95. [4] Narayana, Darapaneni, T. S. S. R. K. Rao, Some remarks on quasi- Chebyshev subspaces. J. Math. Anal. Appl. 321 (2006), no. 1, 193{197. [5] I. Singer, The theory of best approximation and functional analysis. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 13. 1974. [6] I. Singer, Best approximation in normed linear spaces by elements of linear subspaces. Springer-Verlag, New York-Berlin 1970. 4
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