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.
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Translated from Matematicheskie Zametki, Vol. 17, No. 2, pp. 307–318, February, 1975.
In conclusion the author expresses his deep gratitude to Yu. A. Shashkin for his many valuable remarks.
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Ustinov, G.M. Properties of subspaces of the space of affine functions. Mathematical Notes of the Academy of Sciences of the USSR 17, 177–182 (1975). https://doi.org/10.1007/BF01161877
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DOI: https://doi.org/10.1007/BF01161877