13 papers
The Krengel's theorem for compact operators between locally solid vector lattices
Omid Zabeti
Suppose is a locally solid vector lattice. It is known that there are several non-equivalent notions for compact operators on . Furthermore, notion of the -property in $…
The Grothendieck property from an ordered point of view
Omid Zabeti
In this note, we consider several notions related to the Grothendieck property. Among them, we introduce the notion "unbounded Grothendieck property" in a Banach lattice as an unbo…
Bounded orthomorphisms between locally solid vector lattices
Raheleh Sabbagh, Omid Zabeti
The main aim of the present note is to consider bounded orthomorphisms between locally solid vector lattices. We establish a version of the remarkable Zannen theorem regarding equi…
The Banach-Saks property from a locally solid vector lattice point of view
Omid Zabeti
The aim of this note is to consider different notions for the Banach-Saks property in locally solid vector lattices as an extension for the known concepts of the Banach-Saks proper…
Unbounded continuous operators and unbounded Banach-Saks property in Banach lattices
Omid Zabeti
Motivated by the equivalent definition of a continuous operator between Banach spaces in terms of weakly null nets, we introduce unbounded continuous operators by replacing weak co…
Topological lattice rings with -property
Omid Zabeti
Motivated by the recent definition of -property in locally solid vector lattices [O. Zabeti, arXiv: 1912.00141v2 [math.FA]], in this note, we try to investigate those results i…