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Title: Order compact and unbounded order compact operators
Authors: Erkursun Ozcan, Nazife
Gezer, Niyazi Anil
Özdemir, Şaziye Ece
Urganci, Irem Mesude
Keywords: Compact operator
unbounded order convergence
vector lattice
Publisher: Scientific Technical Research Council Turkey-Tubitak
Abstract: 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. Banach lattices can be equipped with various canonical convergence structures such as order, relatively uniform, unbounded order and unbounded norm convergences. Although some of these convergences are not topological, they share the common property that the underlying order structure plays a dominant role in deriving properties related to operators acting on these lattices. The notion of unbounded order convergence was initially introduced in [13] under the name individual convergence, and, ?uo-convergence? was proposed firstly in [7]. Recently in [4, 6, 8?11, 17], see also the references therein, further properties of various types of unbounded convergences are investigated. In the present paper, we study compactness properties of operators between vector lattices by utilizing
ISSN: 1300-0098
Appears in Collections:Fen-Edebiyat Fakültesi Koleksiyonu
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
TR Dizin İndeksli Yayınlar Koleksiyonu / TR Dizin Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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