About the class of ordered limited operators
We give a brief survey of recent results of order limited operators related to some properties on Banach lattices.
Abstract characterization of Orlicz-Kantorovich lattices associated with an -valued measure
An abstract characterization of Orlicz-Kantorovich lattices constructed by a measure with values in the ring of measurable functions is presented.
Acknowledgement of priority: Separable quotients of Banach spaces.
In previous papers, it is proved, among other things, that every infinite dimensional sigma-Dedekind complete Banach lattice has a separable quotient. It has come to my attention that L. Weis proved this result without assuming sigma-Dedekind completeness; the proof is based, however, on the deep theorem of J. Hagler and W.B. Johnson concerning the structure of dual balls of Banach spaces and therefore cannot be applied simply to the case of locally convex solid topologically complete Riesz spaces....
Almost demi Dunford--Pettis operators on Banach lattices
We introduce new concept of almost demi Dunford–Pettis operators. Let be a Banach lattice. An operator from into is said to be almost demi Dunford–Pettis if, for every sequence in such that in and as , we have as . In addition, we study some properties of this class of operators and its relationships with others known operators.
AM-Compactness of some classes of operators
We characterize Banach lattices on which each regular order weakly compact (resp. b-weakly compact, almost Dunford-Pettis, Dunford-Pettis) operator is AM-compact.
An absolute continuity for positive operators on Banach lattices.
An answer to a question of Cao, Reilly and Xiong
We present a simple proof of a Banach-Stone type Theorem. The method used in the proof also provides an answer to a conjecture of Cao, Reilly and Xiong.
An embedding of the algebra of order bounded operators on a Dedekind complete Banach lattice.
An exponential law for regular ordered Banach spaces
An Inequality Related to the Uniform Convexity in Banach Spaces
Application of sets to some classes of operators
The paper contains some applications of the notion of sets to several classes of operators on Banach lattices. In particular, we introduce and study the class of order -Dunford-Pettis operators, that is, operators from a Banach space into a Banach lattice whose adjoint maps order bounded subsets to an sets. As a sequence characterization of such operators, we see that an operator from a Banach space into a Banach lattice is order -Dunford-Pettis, if and only if for for every weakly null...
Application of Rademacher systems to operator characterizations of Banach lattices
Approximation of positive operators and continuity of the spectral radius. II.
Asymptotic periodicity of the iterates of positive contractions on Banach lattices
Attractors and asymptotic periodicity of positive operators on Banach lattices.