The Chebyshev point of a system of translations of subspaces of a Banach space. (English. Russian original) Zbl 0212.45704
Math. Notes 8(1970), 485-491 (1971); translation from Mat. Zametki 8, 29-40 (1970).
MSC:
46B99 | Normed linear spaces and Banach spaces; Banach lattices |
41A50 | Best approximation, Chebyshev systems |
41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |
References:
[1] | S. I. Zukhovitskii and L. I. Avdeeva, Linear and Convex Programming [in Russian], Moscow (1964). |
[2] | A. L. Garkavi, Chebyshev Optimal Solutions of Systems of Linear Equations in Conjunction with an Infinite Number of Inequalities [in Russian], Collection of Mathematical Articles, V. V. Kuibyshev Military Engineering Academy, 3-6 (1968). |
[3] | M. Krein and V. Schmuljan, ?On regulary convex sets in the space conjugate to a Banach space,? Ann. of Math.,41, 556-583 (1940). · Zbl 0024.41305 · doi:10.2307/1968735 |
[4] | N. Dunford and J. T. Schwartz, Linear Operators, General Theory, Interscience, New York (1964). |
[5] | A. L. Garkavi, ?A duality theorem concerning approximations by elements of convex sets,? Uspekhi Matem. Nauk,16, No. 4, 141-145 (1961). |
[6] | A. L. Garkavi, ?Best approximation by elements of a class of infinite-dimensional subspaces,? Matem. Sb.,62, No. 1, 101-120 (1963). · Zbl 0123.09104 |
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