SPACES OF u tau-DUNFORD-PETTIS AND u tau-COMPACT OPERATORS ON LOCALLY SOLID VECTOR LATTICES

Date

2019-01-01

Author

ERKURŞUN ÖZCAN, NAZİFE
Gezer, Niyazi Anıl
Zabeti, Omid

Metadata

Show full item record

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

Item Usage Stats

137
views

0
downloads

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.

Subject Keywords

Locally solid vector lattice, U tau-compact operator, U tau-Dunford-Pettis operator, U-tau-convergence

URI

https://hdl.handle.net/11511/54296

Journal

MATEMATICKI VESNIK

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.
Orbits of groups generated by transvections over F-2 Seven, Ahmet İrfan (Springer Science and Business Media LLC, 2005-06-01) Let V be a finite dimensional vector space over the two element field. We compute orbits for the linear action of groups generated by transvections with respect to a certain class of bilinear forms on V. n particular, we compute orbits that are in bijection with connected components of real double Bruhat cells in semisimple groups, extending results of M. Gekhtman, B. Shapiro, M. Shapiro, A. Vainshtein and A. Zelevinsky.
o tau-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces Alpay, Safak; Emelyanov, Eduard; Gorokhova, Svetlana (2022-06-01) 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...
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

N. ERKURŞUN ÖZCAN, N. A. Gezer, and O. Zabeti, “SPACES OF u tau-DUNFORD-PETTIS AND u tau-COMPACT OPERATORS ON LOCALLY SOLID VECTOR LATTICES,” MATEMATICKI VESNIK, pp. 351–358, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54296.