O. Zabeti

activity

20112026

most citedUnbounded continuous operators in Banach lattices

3 citations · 6 across the 24 of their papers we have counts for

collaborators

29 papers

math.FA2026

A Note on Unbounded Convergences in Fremlin Projective Tensor Products

Omid Zabeti

We prove that the Fremlin projective tensor product of Banach lattices preserves unbounded norm convergence and unbounded absolute weak convergence of elementary tensors without an…

math.FA2026

Fremlin tensor product of Banach lattices and unbounded convergences

Omid Zabeti

Let $E$ and $F$ be Banach lattices. In this short note, we consider several conditions under them, the Fremlin projective tensor product $E \otimes F$ respects either the u…

math.FA2024

A topology on the Fremlin tensor product of locally convex-solid vector lattices

Omid Zabeti

Suppose E and F are locally convex-solid vector lattices. Although we have a suitable vector lattice structure for the tensor product E and F (known as the Fremlin tensor product a…

math.FA2024

Order Continuous and Topological Representations of Archimedean Vector Lattices via $S (X)$ -spaces

Omid Zabeti

For an arbitrary topological space $X$ , assume that $S (X)$ is the vector lattice of all equivalence classes of real-valued continuous functions on open dense subsets of $X$ ; it is…

math.FA2023

Fremlin tensor product behaves well with the unbounded order convergence

Omid Zabeti

Suppose $Σ$ is a topological space and $S (Σ)$ is the vector lattice of all equivalent classes of continuous real-valued functions defined on open dense subsets of $Σ$ . In this pape…

math.FA2022

Unbounded Banach-Saks operators and unbounded Grothendieck operators on Banach lattices

Omid Zabeti

Suppose $E$ is a Banach lattice. Recently, there have been some motivating contexts regarding the known Banach-Saks property and the Grothendieck property from an order point of vi…

math.FA2022

The Krengel's theorem for compact operators between locally solid vector lattices

Omid Zabeti

Suppose $X$ is a locally solid vector lattice. It is known that there are several non-equivalent notions for compact operators on $X$ . Furthermore, notion of the $A M$ -property in $…

math.FA2021

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…

math.FA2020

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…

math.FA2020

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…

math.FA2020

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…

math.FA2020

Topological lattice rings with $A M$ -property

Omid Zabeti

Motivated by the recent definition of $A M$ -property in locally solid vector lattices [O. Zabeti, arXiv: 1912.00141v2 [math.FA]], in this note, we try to investigate those results i…

math.FA2019

$A M$ -spaces from a locally solid vector lattice point of view with applications

Omid Zabeti

Suppose $X$ is a locally solid vector lattice. In this paper, we introduce the notion " $A M$ -property" in $X$ as an extension for $A M$ -spaces in the category of all Banach lattices.…

math.FA2019★ 3 cited

Unbounded continuous operators 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 two types of continuous operators between Banach la…

math.FA2018★ 1 cited

Lattice structure on bounded homomorphisms between topological lattice rings

Omid Zabeti

Suppose $X$ is a locally solid lattice ring. It is known that there are three classes of bounded group homomorphisms on $X$ whose topological structures make them again topological…

math.FA2018

A few remarks on bounded homomorphisms acting on topological lattice groups and topological rings

Omid Zabeti

Suppose $G$ is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on $G$ which have topological structures. In this paper, ou…

math.FA2018

On the lattice structure of the space of all Bochner integrable Banach lattice-valued functions

Omid Zabeti

Suppose $(X, Σ, μ)$ is a finite measure space, $E$ is a Banach lattice, and $B (X, E, μ)$ is the space of all Bochner integrable $E$ -valued functions. In this note, we show that $B(X,E,…

math.FA2018

$uτ$ -continuous operators on locally solid vector lattices

Omid Zabeti, Akbar Bahramnezhad

In this note, we consider the space of all continuous operators with respect to the unbounded topology on locally solid vector lattices. We investigate whether this space forms a b…

math.FA2017

Spaces of $uτ$ -Dunford-Pettis and $uτ$ -Compact Operators on Locally Solid Vector Lattices

Nazife Erkursun Ozcan, Niyazi Anil Gezer, Omid Zabeti

Suppose $X$ is a locally solid vector lattice. It is known that there are several non-equivalent spaces of bounded operators on $X$ . In this paper, we consider some situations unde…

math.FA2017★ 2 cited

Dunford-Pettis and Compact Operators Based on Unbounded Absolute Weak Convergence

Nazife Erkursun Ozcan, Niyazi Anil Gezer, Omid Zabeti

In this paper, using the concept of unbounded absolute weak convergence ( $u a w$ -convergence, for short) in a Banach lattice, we define two classes of continuous operators, named $ua…

math.FA2016

Topological algebras of locally solid vector subspaces of order bounded operators

Omid Zabeti

Let E be a locally solid vector lattice. In this paper, we consider two particular vector subspaces of the space of all order bounded operators on E. With the aid of two appropriat…

math.FA2016

A few remarks on boundedness in topological modules and topological groups

Omid Zabeti

Let X, Y, and Z be topological modules over a topological ring $R$ . In the first part of the paper, we introduce three different classes of bounded bigroup homomorphisms from $X\ti…

math.FA2016

Unbounded absolute weak convergence in Banach lattices

Omid Zabeti

Several recent papers investigated unbounded versions of order and norm convergences in Banach lattices. In this paper, we study the unbounded variant of weak convergence and its r…

math.GN2015

Topological Groups of Bounded Homomorphisms on a Topological Group

Ljubisa D. R. Kocinac, Omid Zabeti

We consider a few types of bounded homomorphisms on a topological group. These classes of bounded homomorphisms are, in a sense, weaker than the class of continuous homomorphisms.…

A Note on Unbounded Convergences in Fremlin Projective Tensor Products

Fremlin tensor product of Banach lattices and unbounded convergences

A topology on the Fremlin tensor product of locally convex-solid vector lattices

Order Continuous and Topological Representations of Archimedean Vector Lattices via S(X)-spaces

Fremlin tensor product behaves well with the unbounded order convergence

Unbounded Banach-Saks operators and unbounded Grothendieck operators on Banach lattices

The Krengel's theorem for compact operators between locally solid vector lattices

The Grothendieck property from an ordered point of view

Bounded orthomorphisms between locally solid vector lattices

The Banach-Saks property from a locally solid vector lattice point of view

Unbounded continuous operators and unbounded Banach-Saks property in Banach lattices

Topological lattice rings with AM-property

AM-spaces from a locally solid vector lattice point of view with applications

Unbounded continuous operators in Banach lattices

Lattice structure on bounded homomorphisms between topological lattice rings

A few remarks on bounded homomorphisms acting on topological lattice groups and topological rings

On the lattice structure of the space of all Bochner integrable Banach lattice-valued functions

uτ-continuous operators on locally solid vector lattices

Spaces of uτ-Dunford-Pettis and uτ-Compact Operators on Locally Solid Vector Lattices

Dunford-Pettis and Compact Operators Based on Unbounded Absolute Weak Convergence

Topological algebras of locally solid vector subspaces of order bounded operators

A few remarks on boundedness in topological modules and topological groups

Unbounded absolute weak convergence in Banach lattices

Topological Groups of Bounded Homomorphisms on a Topological Group

Order Continuous and Topological Representations of Archimedean Vector Lattices via $S (X)$ -spaces

Topological lattice rings with $A M$ -property

$A M$ -spaces from a locally solid vector lattice point of view with applications

$uτ$ -continuous operators on locally solid vector lattices

Spaces of $uτ$ -Dunford-Pettis and $uτ$ -Compact Operators on Locally Solid Vector Lattices