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On some ergodic properties for continuous and affine functions

Charles J. K. Batty (1978)

Annales de l'institut Fourier

Two problems posed by Choquet and Foias are solved:(i) Let T be a positive linear operator on the space C ( X ) of continuous real-valued functions on a compact Hausdorff space X . It is shown that if n - 1 r = 0 n - 1 T r 1 converges pointwise to a continuous limit, then the convergence is uniform on X .(ii) An example is given of a Choquet simplex K and a positive linear operator T on the space A ( K ) of continuous affine real-valued functions on K , such that inf { ( T n 1 ) ( x ) : n } < 1 for each x in K , but T n 1 does not converge to 0.

On the class of order almost L-weakly compact operators

Kamal El Fahri, Hassan Khabaoui, Jawad H'michane (2022)

Commentationes Mathematicae Universitatis Carolinae

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.

On the class of order Dunford-Pettis operators

Khalid Bouras, Abdelmonaim El Kaddouri, Jawad H'michane, Mohammed Moussa (2013)

Mathematica Bohemica

We characterize Banach lattices E and F on which the adjoint of each operator from E into F which is order Dunford-Pettis and weak Dunford-Pettis, is Dunford-Pettis. More precisely, we show that if E and F are two Banach lattices then each order Dunford-Pettis and weak Dunford-Pettis operator T from E into F has an adjoint Dunford-Pettis operator T ' from F ' into E ' if, and only if, the norm of E ' is order continuous or F ' has the Schur property. As a consequence we show that, if E and F are two Banach...

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