On the convergence of nonexpansive operators in a space of continuous abstract functions

P. P. Korovkin, “On the convergence of positive linear operators in the space of continuous functions,” Dokl. Akad. Nauk SSSR,90, No. 6, 961–964 (1953). Yu. A. Shashkin, “Korovkin systems in spaces of continuous functions,” Izv. Akad. Nauk SSSR, Ser. Matem.,26, No. 4, 495–512 (1962). V. K. Dzyadyk, “On the approximation of functions by positive linear operators and by singular integrals,” Matem. Sb.,70, No. 4, 508–517 (1966). V. S. Klimov, M. A. Krasnosel'skii, and E. A. Lifshits, “Points of smoothness of a cone and the convergence of positive functionals and operators,” Trudy Moskov. Matem. Obshch.,15, 55–69 (1966). M. A. Krasnosel'skii and E. A. Lifshits, “The convergence principle for sequences of positive linear operators,” Studia Math.,31, No. 5, 455–468 (1968). D. E. Wulbert, “Convergence of operators and Korovkin's theorem,” J. Approxim. Theory,1, 381–390 (1968). Yu. A. Shashkin, “On the convergence of nonexpansive operators,” Mathematica,11, No. 2, 355–360 (1969). V. S. Rublev, “On a special class of finite-dimensional subspaces of a Banach space,” Dokl. Akad. Nauk SSSR,184, No. 5, 1038–1040 (1969). V. S. Rublev, “On saturated and completely saturated subspaces of certain coordinate spaces,” Dokl. Akad. Nauk SSSR,188, No. 2, 290–293 (1969). M. Gowurin, “Über die Stieltjessche Integration abstrakter Funktionen,” Fund. Math.,27, 254–268 (1936). C. Foias and I. Singer, “Linear operators in spaces of vector-valued functions,” Rev. Roumaine Math. Pures et Appl.,V, 729–752 (1960). J. Batt and H. König, “Darstellung lineares Transformationen,” Arch. Math.,X, 273–287 (1959). J. Batt and E. J. Berg, “Linear bounded transformations on the space of continuous functions,” J. Funct. Anal.,4, No. 2, 215–239 (1969). N. Dunford and J. T. Schwartz, Linear Operators. I General Theory, Interscience, New York, (1958). I. Singer, “La meilleure approximations des functions abstractes,” Rev. Roumaine Math. Pures et Appl.,II, 245–262 (1957). M. M. Day, Normed Linear Spaces, Springer-Verlag, Berlin-Göttingen-Heidelberg (1962). L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces [in Russian], Fizmatgiz, Moscow (1959). J. Dugundji, “An extension of Tietze's theorem,” Pacific J. Math.,1, No. 3, 353–367 (1951). M. P. Ulanov, “Linear functionals on certain spaces of abstract functions,” Sibirsk. Matem. Zh.,IX, No. 2, 402–409 (1968).