Order compact and unbounded order compact operators

Özcan, Nazife Erkurşun; Gezer, Niyazi Anıl; Özdemir, Şaziye Ece; Urganci, Irem Mesude

doi:10.3906/mat-2004-68

Cited by 6 publications

(4 citation statements)

References 13 publications

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Order By: Relevance

“…We recall that an operator T : X → Y between two vector lattices X and Y is said to be order compact, see [13], if for every order bounded net x α in X there exists a subnet x α β and y ∈ Y such that T x α β o − → y in Y .…”

Section: Compact Operators Between Pseudonormed Vector Latticesmentioning

confidence: 99%

On Some Aspects of Pseudonorm Compact and Montel Operators on Locally Solid Vector Lattices

Erkurşun-Özcan,

Gezer

2019

Preprint

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Unbounded convergences have been applied successfully to locally solid topologies on vector lattices. In the present paper, we first expose several properties of various classes of Riesz pseudonorms on vector lattices. We accomplish this by abstracting some generalities of the norm of an AM -space with strong norm unit to locally solid topologies induced by a pseudonorm. By using these classes of pseudonorms, we study compactness properties of operators (not necessarily linear) between locally solid (not necessarily Hausdorff) topologies. We study new classes of operators such as pseudonorm compact, pseudosemicompact and pseudo-AM -compact operators as well as the classical Montel operators.

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Section: Compact Operators Between Pseudonormed Vector Latticesmentioning

confidence: 99%

On Some Aspects of Pseudonorm Compact and Montel Operators on Locally Solid Vector Lattices

Erkurşun-Özcan,

Gezer

2019

Preprint

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“…However, certain types of continuous operators, such as statistical order continuous operators, have been defined with respect to order convergence (cf. [6,8,16]). The aim of this study is to introduce the notion of statistically compact operators on Riesz spaces, as there is currently no comprehensive study of compact operators in the theory of Riesz space with respect to statistical convergence.…”

Section: Introductionmentioning

confidence: 99%

Statistically order compact operators on Riesz spaces

Aydın

2024

Hacettepe Journal of Mathematics and Statistics

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In this paper, we state and establish the concept of compact operators defined between Riesz spaces with respect to statistical order convergence. An operator mapping any statistical order bounded sequence to a sequence with a statistical order convergent subsequence between Riesz spaces is called statistical order compact. Moreover, we also define the notion of statistical M-weakly compact operators. By applying these nontopological concepts, we obtain some new results about these operators.

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“…Various versions of Banach lattice properties like a property to be a KB-space were investigated recently (see, e.g., [1,6,7,8,9,12,13,14,17,18,20,21,22,23,25,27,29,30,31]). In the present paper we continue the study of operator versions of several topological/order properties, focusing on locally solid lattices.…”

Section: Introductionmentioning

confidence: 99%

The $oτ$-continuous, Lebesgue, KB, and Levi operators between vector lattices and topological vector spaces

Alpay¹,

Emelyanov²,

Gorokhova³

2021

Preprint

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We investigate the oτ -continuous/bounded/compact and Lebesgue operators from vector lattices to topological vector spaces; the KB 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.

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Order compact and unbounded order compact operators

Cited by 6 publications

References 13 publications

On Some Aspects of Pseudonorm Compact and Montel Operators on Locally Solid Vector Lattices

On Some Aspects of Pseudonorm Compact and Montel Operators on Locally Solid Vector Lattices

Statistically order compact operators on Riesz spaces

The $oτ$-continuous, Lebesgue, KB, and Levi operators between vector lattices and topological vector spaces

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