On the fixing of values of sequences of seminorms

Theorems on the fixing of values of sequences of continuous seminorms on certain sets in Banach spaces are proved, enabling one to obtain new results on the asymptotic behavior of approximations of individual functions and on the convergence of interpolation processes on classes of functions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 467–474, April, 1992.