/pdf/antiproksiminalnye-mnozhestva-v-prostranstvakh-nepreryvnykh-3dr9ef8qlj.pdf

Антипроксиминальные множества в пространствах непрерывных функций@@@Antiproximinal sets in spaces of continuous functions

Antiproximinal Norms in Banach Spaces

Closed convex bounded antiproximinal bodies are constructed in the infinite-dimensional spacesC(Q), C
0(T), L∞(S, S, μ), andB(S), whereQ is a topological space andT is a locally compact Hausdorff space. It is shown that there are no closed bounded antiproximinal sets in Banach spaces with the Radon-Nikodym property.

Antiproximinal sets in spaces of continuous functions

Antiproximinal Sets in Banach Spaces of Continuous Vector-Valued Functions☆☆☆

i. A. Ya. Dubovitskii and A. A. Milyutin, "Problems on the extremum in the presence of restrictions," Zh. Vyshicl. Mat. Mat. Fiz., 5, No. 3, 395-453 (1965). 2. S. D. Fischer, "Solution of some nonlinear variational problems in L~ and the problem of minimum curvature," Arch. Rational Mech. Anal., 61, No. 3, 291-305 (1976). 3. S. D. Fisher and J. W. Jerome, "Minimum norm extremals in function spaces," Lect. Notes Math., 479, Springer-Verlag, Berlin--Heidelberg--New York (1975). 4. G. Aronsson, "Pontryagin's maximum principle and a minimax problem," Math. Scand., 29, No. i, 55-71 (1971). 5. G. Aronsson, "Perfect splines and nonlinear optimal control theory," J. Approx. Theory, 25, No. 2, 142-152 (1979). 6. E. E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press (1971). 7. H. Cartan, Differential Forms, HM (1970). 8. E. B. Li and L. Markus, Foundations of the Theory of Optimal Control [in Russian], Nauka, Moscow (1972). 9. M. Altman, "A fixed point theorem in Banach space," Bull. Acad. Polonaise, C1 III, 5, No. 2, 89-92 (1957). i0. P.-J. Laurent, Approximation and Optimization [Russian translation], Mir, Moscow (1975).

http://rd.springer.com/content/pdf/10.1007%2FBF01157060.pdf

Ş. Cobzaş

Papers

Antiproximinal sets in Banach spaces of \(c_0\)-type