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Approximation by finite rank operators. (English) Zbl 0521.41017


MSC:

41A36 Approximation by positive operators
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

Keywords:

proximal sets
Full Text: DOI

References:

[1] Alfsen, E. M.; Effros, E. G., Structure in real Banach spaces, I, Ann of Math. II. Ser., 96, 98-128 (1972) · Zbl 0248.46019
[2] Amir, D.; Deutsch, F., Approximation by certain subspaces of the Banach space of continuous vector valued functions, J. Approx. Theory, 27, 1-17 (1979)
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[4] Brown, A. L., Best \(n\)-dimensional approximation of functions, (Proc. London Math. Soc., 14 (1964)), 577-594 · Zbl 0129.04702
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[6] Dunford, N.; Schwartz, J. T., Linear Operators, I (1958), Interscience: Interscience New York · Zbl 0084.10402
[7] Fakhoury, H., Approximation des bornés d’un espace de Banach par des compacts et applications á l’approximation des opérateurs bornés, J. Approx. Theory, 26, 79-100 (1979) · Zbl 0401.41035
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[10] Holmes, R. B.; Scranton, B. E.; Ward, J. D., Approximation from the space of compact operators and other \(M\)-ideals, Duke Math. J., 39, 1-8 (1972)
[11] Lau, K. S., Approximation by continuous vector-valued functions, Studio Math., 68, 291-298 (1980) · Zbl 0455.41015
[12] Lima, A., \(M\)-ideals of compact operators in classical Banach spaces, Math. Scand., 44, 207-217 (1979) · Zbl 0407.46019
[13] Mach, J., On the proximinality of compact operators with range in \(C(S)\), (Proc. Amer. Math. Soc., 72 (1978)), 99-104 · Zbl 0402.41009
[14] Mach, J., Best simultaneous approximations of bounded functions with values in certain Banach spaces, Math. Ann., 240, 157-164 (1979) · Zbl 0388.41014
[15] Mach, J.; Ward, J. D., Approximation by compact operators in certain Banach spaces, J. Approx. Theory, 23, 274-286 (1978) · Zbl 0399.41030
[16] Olsen, C. L., Extreme points and finite rank operators in the set of compact approximants, Indiana Univ. Math. J., 24, 409-416 (1979) · Zbl 0301.47023
[17] Saatkamp, K., \(M\)-Videals of compact operators, Math. Z., 158, 253-263 (1978) · Zbl 0354.47017
[18] Schaeffer, H. H., Banach Lattices and Positive Operators (1979), Springer-Verlag: Springer-Verlag Berlin, Heidelberg/New York
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