arXiv subjects

Omid Zabeti

Publications and source records attributed to Omid Zabeti.

29 records · Page 2Linked to original sources

arXiv2018

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

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 under which these classes of bounded operators form locally solid vector lattices. In addition, we generalize some notions of $uaw$-Dunford-Pettis operators and $uaw$-compact operators defined on a Banach lattice to general theme of locally solid vector lattices. With the aid of appropriate topologies, we investigate some relations between topological and lattice structures of these operators. In particular, we characterize those spaces for which these concepts of operators and the corresponding classes of bounded ones coincide.

math.FA↗

arXiv2018

$uτ$-continuous operators on locally solid vector lattices

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 band. In addition, we look into some situations under which, the modulus of a continuous operator has the same property. Some examples are given to make the context more understandable.

math.FA↗

arXiv2017

Topological Modules of Bounded Bigroup Homomorphisms on a Topological Module

Let X, Y, and Z be topological modules over a topological ring R. In this paper, we introduce three different classes of bounded bigroup homomorphisms from X \times Y into Z with respect to the three different uniform convergence topologies. We show that the operations of addition and module multiplication are continuous for each class of bounded bigroup homomorphisms. Also, we investigate whether each class of bounded bigroup homomorphisms is uniformly complete.

math.FA↗

arXiv2017

A few remarks on boundedness in topological modules and topological groups

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 $X\times Y$ into $Z$ with respect to the three different uniform convergence topologies. We show that these spaces form again topological modules over $R$. In the second part, we characterize bounded sets in the arbitrary product of topological groups with respect to the both product and box topologies.

math.FA↗

arXiv2017

Unbounded absolute weak convergence in Banach lattices

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 relationship with other convergences. In particular, we characterize order continuous Banach lattices and reflexive Banach lattices in terms of this convergence.

math.FA↗

arXiv2016

Topological algebras of locally solid vector subspaces of order bounded operators

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 appropriate topologies, we show that under some conditions, they establish both, locally solid vector lattices and topologically complete topological algebras.

math.FA↗

arXiv2015

A few remarks on bounded operators on topological vector spaces

We give a few observations on different types of bounded operators on a topological vector space X and their relations with compact operators on X. In particular, we investigate when these bounded operators coincide with compact operators. We also consider similar types of bounded bilinear mappings between topological vector spaces. Some properties of tensor product operators between locally convex spaces are established. In the last part of the paper we deal with operators on topological Riesz spaces.

math.FA↗

arXiv2015

Topological Groups of Bounded Homomorphisms on a Topological Group

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. We show that with appropriate topologies each class of these homomorphisms on a complete topological group forms a complete topological group.

math.GN↗

arXiv2014

Continuous Functions that Cut the Real Axis Very Often

We consider continuous functions f : [0,1] \to R that cut the real axis at every point of a measurable set of positive measure and we construct examples where f fails to have bounded variation, and at the opposite end, where f admits derivatives of all orders.

math.CA↗

arXiv2014

Extended eigenvalues for Cesàro operators

A complex scalar $λ$ is said to be an extended eigenvalue of a bounded linear operator $T$ on a complex Banach space if there is a nonzero operator $X$ such that $TX= λXT.$ Such an operator $X$ is called an extended eigenoperator of $T$ corresponding to the extended eigenvalue $λ.$ The purpose of this paper is to give a description of the extended eigenvalues for the discrete Cesàro operator $C_0,$ the finite continuous Cesàro operator $C_1$ and the infinite continuous Cesàro operator $C_\infty$ defined on the complex Banach spaces $\ell^p,$ $L^p[0,1]$ and $L^p[0,\infty)$ for $1 < p <\infty$ by the expressions \begin{align*} (C_0f)(n) \colon & = \frac{1}{n+1} \sum_{k=0}^n f(k),\\ (C_1f)(x) \colon & = \frac{1}{x} \int_0^x f(t)\,dt,\\ (C_\infty f)(x) \colon & = \frac{1}{x} \int_0^x f(t)\,dt. \end{align*} It is shown that the set of extended eigenvalues for $C_0$ is the interval $[1,\infty),$ for $C_1$ it is the interval $(0,1],$ and for $C_\infty$ it reduces to the singleton $\{1\}.$

math.FA↗

arXiv2013

Fremlin Tensor Products of Concavifications of Banach Lattices

Suppose that $E$ is a uniformly complete vector lattice and $p_1,..., p_n$ are positive reals. We prove that the diagonal of the Fremlin projective tensor product of $E_{(p_1)},..., E_{(p_n)}$ can be identified with $E_{(p)}$ where $p = p_1+...+p_n$ and $E_{(p)}$ stands for the $p$-concavification of $E$. We also provide a variant of this result for Banach lattices. This extends the main result of [BBPTT].

math.FA↗