Properties of subspaces of the space of affine functions

G. M. Ustinov

Institute of Mathematics and Mechanics, Ural Branch of the AS of USSR

Abstract: Conditions are presented for weak (strong) convergence, in the entire space $A(x)$, of a sequence of positive operators to a fixed operator $S$ on the basis of its weak (strong) convergence to $S$ in a subspace. The criterion of Bauer's simplex is presented.

UDC: 513.88

Received: 01.10.1973

 English version: Mathematical Notes, 1975, 17:2, 177–182

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