Strong uniqueness of best approximations in spaces of bounded linear operators

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 c_0 to c_0 is characterized by the strict Kolmogorov's condition. Some recent results due to Lewicki and others are extended and improved.