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 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
