Geodesic
Properties of subspaces of the space of affine functions
Matematičeskie zametki, Tome 17 (1975) no. 2, pp. 307-318

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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. 
@article{MZM_1975_17_2_a13,
     author = {G. M. Ustinov},
     title = {Properties of subspaces of the space of affine functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {307--318},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a13/}
}
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G. M. Ustinov. Properties of subspaces of the space of affine functions. Matematičeskie zametki, Tome 17 (1975) no. 2, pp. 307-318. http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a13/