o tau-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces

Download

index.pdf

Date

2022-06-01

Author

Alpay, Safak
Emelyanov, Eduard
Gorokhova, Svetlana

Metadata

Show full item record

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

Item Usage Stats

228
views

79
downloads

We investigate o tau-continuous/bounded/compact and Lebesgue operators from vector lattices to topological vector spaces; the Kantorovich-Banach operators between locally solid lattices and topological vector spaces; and the Levi operators from locally solid lattices to vector lattices. The main idea of operator versions of notions related to vector lattices lies in redistributing topological and order properties of a topological vector lattice between the domain and range of an operator under investigation. Domination properties for these classes of operators are studied.

Subject Keywords

Topological vector space, locally solid lattice, Banach lattice, order convergence, domination property, adjoint operator, BANACH-LATTICES, UO-CONVERGENCE, DUNFORD-PETTIS, COMPACT

URI

https://hdl.handle.net/11511/97292

Journal

RESULTS IN MATHEMATICS

DOI

https://doi.org/10.1007/s00025-022-01650-3

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

uτ-Convergence in locally solid vector lattices Dabboorasad, Yousef A M; Emel’yanov, Eduard; Department of Mathematics (2018) We say that a net (xα) in a locally solid vector lattice (X,τ) is uτ-convergent to a vector x ∈ X if
ON OPERATORS OF STRONG TYPE B Alpay, Safak (2012-10-01) We discuss operators of strong type B between a Banach lattice and a Banach space and give necessary and sufficient conditions for this class of operators to coincide with weakly compact operators.
SPACES OF u tau-DUNFORD-PETTIS AND u tau-COMPACT OPERATORS ON LOCALLY SOLID VECTOR LATTICES ERKURŞUN ÖZCAN, NAZİFE; Gezer, Niyazi Anıl; Zabeti, Omid (2019-01-01) 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 to...
Bibounded uo-convergence and b-property in vector lattices Alpay, Safak; Emelyanov, Eduard; Gorokhova, Svetlana (2021-01-01) We define bidual bounded uo-convergence in vector lattices and investigate relations between this convergence and b-property. We prove that for a regular Riesz dual system ⟨ X, X∼⟩ , X has b-property if and only if the order convergence in X agrees with the order convergence in X∼ ∼.
um-Topology in multi-normed vector lattices Dabboorasad, Y. A.; Emelyanov, Eduard; Marabeh, M. A. A. (2018-04-01) Let be a separating family of lattice seminorms on a vector lattice X, then is called a multi-normed vector lattice (or MNVL). We write if for all . A net in an MNVL is said to be unbounded m-convergent (or um-convergent) to x if for all . um-Convergence generalizes un-convergence (Deng et al. in Positivity 21:963-974, 2017; KandiAc et al. in J Math Anal Appl 451:259-279, 2017) and uaw-convergence (Zabeti in Positivity, 2017. doi:10.1007/s11117-017-0524-7), and specializes up-convergence (AydA +/- n et al. ...

Citation Formats

S. Alpay, E. Emelyanov, and S. Gorokhova, “o tau-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces,” RESULTS IN MATHEMATICS, vol. 77, no. 3, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/97292.