O спектре операторов в идеальных пространствах
Two problems posed by Choquet and Foias are solved:(i) Let be a positive linear operator on the space of continuous real-valued functions on a compact Hausdorff space . It is shown that if converges pointwise to a continuous limit, then the convergence is uniform on .(ii) An example is given of a Choquet simplex and a positive linear operator on the space of continuous affine real-valued functions on , such thatfor each in , but does not converge to 0.
In this paper, we introduce and study new concepts of b-L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of KB-spaces.
We introduce a new class of operators that generalizes L-weakly compact operators, which we call order almost L-weakly compact. We give some characterizations of this class and we show that this class of operators satisfies the domination problem.
We characterize Banach lattices and on which the adjoint of each operator from into which is order Dunford-Pettis and weak Dunford-Pettis, is Dunford-Pettis. More precisely, we show that if and are two Banach lattices then each order Dunford-Pettis and weak Dunford-Pettis operator from into has an adjoint Dunford-Pettis operator from into if, and only if, the norm of is order continuous or has the Schur property. As a consequence we show that, if and are two Banach...