Eventually and asymptotically positive semigroups on Banach lattices

Strong convergence for total asymptotically pseudocontractive semigroups in Banach spaces

*Correspondence: [email protected] Department of Mathematics, Yibin University, Yibin, Sichuan 644007, China Abstract In this article, the demiclosedness principle for total asymptotically pseudocontractions in Banach spaces is established. The strong convergence to a common fixed point of total asymptotically pseudocontractive semigroups in Banach spaces is established based on the demiclosednes...

The Positive Fixed Points of Banach Lattices

Let Z be a Banach lattice endowed with positive cone C and an order-continuous norm j.j . Let G be a left-amenable semigroup of positive linear endomorphisms of Z . Then the positive fixed points Co of Z under G form a lattice cone, and their linear span Z0 is a Banach lattice under an order-continuous norm ||.||0 which agrees with |.| on Co. A counterexample shows that under the given conditio...

On Asymptotically Symmetric Banach Spaces

A Banach space X is asymptotically symmetric (a.s.) if for some C <∞, for all m ∈ N, for all bounded sequences (xj)j=1 ⊆ X, 1 ≤ i ≤ m, for all permutations σ of {1, . . . ,m} and all ultrafilters U1, . . . ,Um on N, lim n1,U1 . . . lim nm,Um ∥∥∥∥ m ∑ i=1 xini ∥∥∥∥ ≤ C lim nσ(1),Uσ(1) . . . lim nσ(m),Uσ(m) ∥∥∥∥ m ∑

Some properties of b-weakly compact operators on Banach lattices

In this paper we give some necessary and sufficient conditions for which each Banach lattice  is    space and we study some properties of b-weakly compact operators from a Banach lattice  into a Banach space . We show that every weakly compact operator from a Banach lattice  into a Banach space  is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...

Total quasi-φ-asymptotically nonexpansive semigroups and strong convergence theorems in Banach spaces