Order compact and unbounded order compact operators

URGANCI, İrem Mesude; ERKURŞUN ÖZCAN, Nazife; GEZER, Niyazi Anıl; ÖZDEMİR, Şaziye Ece

doi:10.3906/mat-2004-68

Order compact and unbounded order compact operators

Nazife ERKURŞUN ÖZCAN, (Hacettepe Üniversitesi, Fen Fakültesi, Matematik Bölümü, Ankara, Türkiye)

Niyazi Anıl GEZER, (Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Ankara, Türkiye)

Şaziye Ece ÖZDEMİR, (Pamukkale Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Denizli, Türkiye)

İrem Mesude URGANCI (Gazi Üniversitesi, Matematik Bölümü, Fen Fakültesi, Ankara, Türkiye)

Turkish Journal of Mathematics

7 0

Yıl: 2021 Cilt: 45 Sayı: 2 Sayfa Aralığı: 634 - 646 Metin Dili: İngilizce DOI: 10.3906/mat-2004-68 İndeks Tarihi: 22-09-2021

Order compact and unbounded order compact operators

Öz:

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

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Aliprantis CD, Burkinshaw O. Locally solid Riesz spaces with applications to economics. Mathematical Surveys and Monographs, Vol. 105, Providence, RI, USA: American Mathematical Society, 2003.
[2] Aliprantis CD, Burkinshaw O. Positive operators (reprint of the 1985 original). Dordrecht, Netherlands: Springer, 2006.
[3] Aydın A, Emelyanov EY, Erkurşun Özcan N, Marabeh MAA. Compact-like operators in lattice-normed spaces. Indagationes Mathematicae 2018; 29 (2): 633-656. doi: 10.1016/j.indag.2017.11.002
[4] Azouzi Y. Completeness for vector lattices. Journal of Mathematical Analysis and Applications 2019; 472: 216-230. doi: 10.1016/j.jmaa.2018.11.019
[5] Azouzi Y, Ben Amor MA. On Compact operators between lattice normed spaces. arXiv 2019; 1903.00370v1.
[6] Dabboorasad YAM, Emel’yanov EYu, Marabeh MAA. uτ -convergence in locally solid vector lattices. Positivity 2018; 22: 1065-1080. doi: 10.1007/s11117-018-0559-4
[7] DeMarr R. Partially ordered linear spaces and locally convex linear topological spaces. Illinois Journal of Mathematics 1964; 8: 601-606. doi: 10.1215/ijm/1256059459
[8] Deng Y, O’Brien M, Troitsky VG. Unbounded norm convergence in Banach lattices. Positivity 2017; 21: 963-974. doi: 10.1007/s11117-016-0446-9
[9] Erkurşun-Özcan N, Gezer NA. Unbounded asymptotic equivalences of operator nets with applications. Positivity 2019; 23. doi: 10.1007/s11117-018-0640-z
[10] Gao N, Troitsky VG, Xanthos F. Uo-convergence and its applications to Cesaro means in Banach lattices. Israel Journal of Mathematics 2017; 220: 649-689. doi: 10.1007/s11856-017-1530-y
[11] Gao N, Xanthos F. Unbounded order convergence and application to martingales without probability. Journal of Mathematical Analysis and Applications 2014; 415: 931-947. doi: 10.1016/j.jmaa.2014.01.078
[12] Luxemburg WAJ, Zaanen AC. Riesz Spaces I. Amsterdam, Netherlands: North-Holland Publishing Company, 1971.
[13] Nakano H. Ergodic theorems in semi-ordered linear spaces. Annals of Mathematics 1948; 49 (2): 538-556. doi: 10.2307/1969044
[14] Pliev M. Narrow operators on lattice-normed spaces. Central European Journal of Mathematics 2001; 9 (6): 1276-1287. doi: 10.2478/s11533-011-0090-3
[15] Tucker CT. Homomorphisms of Riesz spaces. Pacific Journal of Mathematics 1974; 55 (1).
[16] Vulikh BZ. Introduction to the theory of partially ordered spaces. Groningen, Netherlands: WoltersNoordhoff Scientific Publications, 1967.
[17] Wickstead AW. Weak and unbounded order convergence in Banach lattices. Journal of the Australian Mathematical Society 1977; 24 (3): 312-319. doi: 10.1017/S1446788700020346
[18] Zaanen AC. Riesz Spaces II. Vol. 30 of North-Holland Mathematical Library. Amsterdam, Netherlands: North-Holland Publishing Company, 1983.

APA	ERKURŞUN ÖZCAN N, GEZER N, ÖZDEMİR Ş, URGANCI İ (2021). Order compact and unbounded order compact operators. , 634 - 646. 10.3906/mat-2004-68
Chicago	ERKURŞUN ÖZCAN Nazife,GEZER Niyazi Anıl,ÖZDEMİR Şaziye Ece,URGANCI İrem Mesude Order compact and unbounded order compact operators. (2021): 634 - 646. 10.3906/mat-2004-68
MLA	ERKURŞUN ÖZCAN Nazife,GEZER Niyazi Anıl,ÖZDEMİR Şaziye Ece,URGANCI İrem Mesude Order compact and unbounded order compact operators. , 2021, ss.634 - 646. 10.3906/mat-2004-68
AMA	ERKURŞUN ÖZCAN N,GEZER N,ÖZDEMİR Ş,URGANCI İ Order compact and unbounded order compact operators. . 2021; 634 - 646. 10.3906/mat-2004-68
Vancouver	ERKURŞUN ÖZCAN N,GEZER N,ÖZDEMİR Ş,URGANCI İ Order compact and unbounded order compact operators. . 2021; 634 - 646. 10.3906/mat-2004-68
IEEE	ERKURŞUN ÖZCAN N,GEZER N,ÖZDEMİR Ş,URGANCI İ "Order compact and unbounded order compact operators." , ss.634 - 646, 2021. 10.3906/mat-2004-68
ISNAD	ERKURŞUN ÖZCAN, Nazife vd. "Order compact and unbounded order compact operators". (2021), 634-646. https://doi.org/10.3906/mat-2004-68

APA	ERKURŞUN ÖZCAN N, GEZER N, ÖZDEMİR Ş, URGANCI İ (2021). Order compact and unbounded order compact operators. Turkish Journal of Mathematics, 45(2), 634 - 646. 10.3906/mat-2004-68
Chicago	ERKURŞUN ÖZCAN Nazife,GEZER Niyazi Anıl,ÖZDEMİR Şaziye Ece,URGANCI İrem Mesude Order compact and unbounded order compact operators. Turkish Journal of Mathematics 45, no.2 (2021): 634 - 646. 10.3906/mat-2004-68
MLA	ERKURŞUN ÖZCAN Nazife,GEZER Niyazi Anıl,ÖZDEMİR Şaziye Ece,URGANCI İrem Mesude Order compact and unbounded order compact operators. Turkish Journal of Mathematics, vol.45, no.2, 2021, ss.634 - 646. 10.3906/mat-2004-68
AMA	ERKURŞUN ÖZCAN N,GEZER N,ÖZDEMİR Ş,URGANCI İ Order compact and unbounded order compact operators. Turkish Journal of Mathematics. 2021; 45(2): 634 - 646. 10.3906/mat-2004-68
Vancouver	ERKURŞUN ÖZCAN N,GEZER N,ÖZDEMİR Ş,URGANCI İ Order compact and unbounded order compact operators. Turkish Journal of Mathematics. 2021; 45(2): 634 - 646. 10.3906/mat-2004-68
IEEE	ERKURŞUN ÖZCAN N,GEZER N,ÖZDEMİR Ş,URGANCI İ "Order compact and unbounded order compact operators." Turkish Journal of Mathematics, 45, ss.634 - 646, 2021. 10.3906/mat-2004-68
ISNAD	ERKURŞUN ÖZCAN, Nazife vd. "Order compact and unbounded order compact operators". Turkish Journal of Mathematics 45/2 (2021), 634-646. https://doi.org/10.3906/mat-2004-68