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Kolmogorov’s type criteria for spaces of compact operators. (English) Zbl 0741.41032
The author gives various theorems on Kolmogorov’s type criteria for spaces of compact operators and proves several results concerning strongly unique best approximation. The characterisations are expressed in a form which is more convenient for applications. Indeed some classical results from the theory of minimal projections due to Cheney and others: (i) E. W. Cheney and K. Price [ Iterationsverf., Numer. Math., Approximationstheorie, Oberwolfach 1968 u. 1969, 115–121 (1970; Zbl 0217.16201)], (ii) E. W. Cheney, P. D. Moris and K. H. Price [J. Approximation Theory 13, 375–391 (1975; Zbl 0312.41010)], (iii) E. W. Cheney and C. Franchetti [Colloq. Math. Soc. János Bolyai 19, 241–253 (1978; Zbl 0421.46004)], are generalised and improved upon.

MSC:
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
46E15 Banach spaces of continuous, differentiable or analytic functions
41A50 Best approximation, Chebyshev systems
41A44 Best constants in approximation theory
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