Asymptotically absorbing nets of positive operators

Emelyanov, Eduard; Erkursun, Nazife

doi:10.3103/s1055134412040025

Cited by 3 publications

(4 citation statements)

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“…The notions of d-martingale and d-L R-nets are well motivated, see [6,7,9,10,12,13,18,20] for their applications. Since operator nets may not be uniformly bounded in the settings of convergences, uniformly bounded n-martingale and n-L R-nets are martingale and L R-nets in the sense of [7,10], respectively.…”

Section: Denote By X *mentioning

confidence: 99%

“…If T is a contraction then the sequence A T k is both n-L R-net and L R-net, in the sense of [6,7,9,10]. Suppose that T is mean ergodic so that…”

Section: Example 16mentioning

confidence: 99%

“…Throughout the present paper, limits are taken over the index λ. We refer the reader to [6,7,[9][10][11]18,20] for expositions on Lotz-Räbiger and martingale nets.…”

Section: Introductionmentioning

confidence: 99%

“…3.2, we prove basic properties of d-Lotz-Räbiger nets and d-martingale nets. One of the purposes of this subsection is to obtain results generalizing some results of [6,7,[9][10][11]18,20] to the settings of unbounded topologies. In Sect.…”

Section: Introductionmentioning

confidence: 99%

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Unbounded asymptotic equivalences of operator nets with applications

Erkurşun-Özcan

Gezer

2019

Positivity

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Present paper deals with applications of asymptotic equivalence relations on operator nets. These relations are defined via unbounded convergences on vector lattices. Given two convergences c and d on a vector lattice, we study d-asymptotic properties of operator nets formed by c-continuous operators. Asymptotic equivalences are known to be useful and extremely important tools to study infinite behaviors of strongly convergent operator nets and continuous semigroups. After giving a general theory, paper focuses on d-martingale and d-Lotz-Räbiger nets.) is said to be a convergence vector lattice. Let J be an order dense ideal, see [1,2] for more on this notion, in the vector lattice (X, c). Following [5], we write x λwe write uc instead of u J c. Prime examples of c are order convergence and norm convergence which are respectively denoted by o and B Niyazi Anıl Gezer

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Section: Denote By X *mentioning

confidence: 99%

“…If T is a contraction then the sequence A T k is both n-L R-net and L R-net, in the sense of [6,7,9,10]. Suppose that T is mean ergodic so that…”

Section: Example 16mentioning

confidence: 99%

“…Throughout the present paper, limits are taken over the index λ. We refer the reader to [6,7,[9][10][11]18,20] for expositions on Lotz-Räbiger and martingale nets.…”

Section: Introductionmentioning

confidence: 99%