Order structure of order-to-topological continuous operator

Authors

Gül SİNEM KELEŞFollow
BAHRİ TURANFollow
BİROL ALTINFollow

Author ORCID Identifier

Gül SİNEM KELEŞ: 0000-0001-5712-239X

BAHRİ TURAN: 0000-0001-5256-1115

BİROL ALTIN: 0000-0002-1085-809X

Abstract

Let J be a vector lattice, and W be a topological vector space. An operator K: J → W is called an order-to-topological continuous operator if u_α → 0 in J implies K(u_α) → 0 in W for each net (u_α) in J. In this study, we examine the order structure of the space of order-to-topological continuous operators in general and the order structure of order-to-norm continuous operators in particular. We study the relationships between order-to-topology continuous operators and other classes of operators, such as order weakly compact and order continuous operators. Moreover, we give solutions to two open problems posed by Jalili et al. (Order-to-topology continuous operators. Positivity 2021; 25: 1313-1322).

DOI

10.55730/1300-0098.3581

Keywords

Banach lattice, vector lattice, order convergent net, order-to-topology continuous operator, order weakly compact operator

First Page

173

Last Page

184

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

KELEŞ, Gül SİNEM; TURAN, BAHRİ; and ALTIN, BİROL (2025) "Order structure of order-to-topological continuous operator," Turkish Journal of Mathematics: Vol. 49: No. 2, Article 3. https://doi.org/10.55730/1300-0098.3581
Available at: https://journals.tubitak.gov.tr/math/vol49/iss2/3