Order compact and unbounded order compact operators

Date

2021-01-01

Author

ERKURŞUN ÖZCAN, NAZİFE
Gezer, Niyazi Anıl
Ozdemir, Saziye Ece
Urganci, Irem Mesude

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We investigate properties of order compact, unbounded order compact and relatively uniformly compact operators acting on vector lattices. An operator is said to be order compact if it maps an arbitrary order bounded net to a net with an order convergent subnet. Analogously, an operator is said to be unbounded order compact if it maps an arbitrary order bounded net to a net with uo-convergent subnet. After exposing the relationships between order compact, unbounded order compact, semicompact and GAM-compact operators; we study those operators mapping an arbitrary order bounded net to a net with a relatively uniformly convergent subnet. By using the nontopological concepts of order and unbounded order convergences, we derive new results related to these classes of operators.

URI

https://hdl.handle.net/11511/90036

Journal

TURKISH JOURNAL OF MATHEMATICS

DOI

https://doi.org/10.3906/mat-2004-68

Collections

Department of Mathematics, Article

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Citation Formats

N. ERKURŞUN ÖZCAN, N. A. Gezer, S. E. Ozdemir, and I. M. Urganci, “Order compact and unbounded order compact operators,” TURKISH JOURNAL OF MATHEMATICS, pp. 634–646, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/90036.