Abstract
The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator spaces. Some results on the strong uniqueness of the best approximation operator from RS-sets are proved and the uniqueness element of a sun in the compact operator space from C0 to C0 is characterized by the strict Kolmogorov’s condition. Some recent results due to Lewicki and others are extended and improved.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lewicki, G., Kolmogorov’s type criteria for spaces of compact operators, J. Approx. Theory, 1991, 64(2): 181–202.
Lewicki, G., Best approximation in spaces of bounded linear operators, Dissertatione Math., 1994, 330, 130.
Lewicki, G., Best approximation in finite dimensional subspaces of L(W, V), J. Approx. Theory, 1995, 81(2): 151–165.
Li, C., Sun sets in spaces of bounded linear operators, Chinese Ann. Math. (in Chinese), 1995, 16A(1): 60–69.
Malbrock, J., Chebyshev subspaces in the space of bounded linear operators from c0 to c0, J. Approx. Theory, 1973, 9(2): 149–164.
Malbrock, J., Best approximation in the space of bounded linear operators from C(X) to C(Y), J. Approx. Theory, 1975, 15(2): 132–142.
Odyniec, W., Lewicki, G., Minimal projections in Banach spaces, Lecture Notes in Mathematics, 1449, Berlin Heidelberg: Springer-Verlag, 1990.
Lewicki, G., On minimal projections onto two dimensional subspaces of l ∞(4), J. Approx. Theory, 1997, 88(1): 92–108.
Lewicki, G., The uniqueness of norm-one projections in spaces of James-type spaces, J. Approx. Theory, 1999, 100(1): 73–93.
Skrzypek, L., Uniqueness of minimal projections in smooth matrix spaces, J. Approx. Theory, 2000, 107(2): 315–336.
He, J. S., Li, C., Strong uniqueness of best approximations from RS-sets in Banach spaces, J. Southeast Univ., 2001, 17(1): 70–72.
Freilich, J. H., Mclaughlin, H. W., Approximation of bounded sets, J. Approx. Theory, 1982, 34(2): 146–158.
Xu, S. Y., Li, C., Characterization of the best simultaneous approximation, Acta Math. Sinica (in Chinese), 1987, 30(3): 528–534.
Amir, D., Uniqueness of best simultaneous approximations and strictly interpolating subspaces, J. Approx. Theory, 1984, 40(3): 196–201.
Cheney, E. W., Introduction to Approximation Theory, New York: McGraw-Hill, 1966.
Ruess, W. M., Stegall, C., Extreme points in duals of operator spaces, Math. Ann., 1982, 261: 535–546.
Yang, W. S., Li, C., Watson G. A., Characterization and uniqueness of nonlinear uniform approximation, Proc. Edinburgh Math. Soc., 1997, 40(3): 473–482.
Li, C., Watson, G. A., Strong uniqueness in restricted rational approximation, J Approx. Theory, 1997, 89(1): 96–113.
Li, C., Wang, X. H., Generalized weight approximation by maximal families with applications, Acta Math. Sinica (New Ser.), 1998,14(sub): 635–646.
Li, C., Watson G. A., On best simultaneous approximation, J Approx. Theory, 1997, 91(2): 332–348.
Braess, D., Nonlinear Approximation Theory, Berlin Heidelberg: Springer-Verlag, 1986.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, C., He, J. Strong uniqueness of best approximations in spaces of bounded linear operators. Sci. China Ser. A-Math. 47, 339–351 (2004). https://doi.org/10.1360/02ys0336
Received:
Issue Date:
DOI: https://doi.org/10.1360/02ys0336