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.
Article Title [Persian]
Best approximation by closed unit balls
Authors [Persian]
H. R. Kamali1; H. Mazaheri2; H. R. Khadezadeh2; H. Ardakani2
1Department of Mathematics,Ardakan Branch,Islamic Azad
university,Ardakan,Iran.
2Faculty of Mathematics, Yazd University, Yazd, Iran.
Abstract [Persian]
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.
Keywords [Persian]
Best approximation، Orthogonality، Closed unit balls، Kadec-Klee property، Shur property
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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