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February 2018 Convergence properties of nets of operators
Fadel Nasaireh, Dorian Popa, Ioan Rasa
Ann. Funct. Anal. 9(1): 1-7 (February 2018). DOI: 10.1215/20088752-2017-0018

Abstract

We consider nets (Tj) of operators acting on complex functions, and we investigate the algebraic and the topological structure of the set {f:Tj(|f|2)|Tjf|20}. Our results extend and improve some known results from the literature, which are connected with Korovkin’s theorem. Applications to Abel–Poisson-type operators and Bernstein-type operators are given.

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Fadel Nasaireh. Dorian Popa. Ioan Rasa. "Convergence properties of nets of operators." Ann. Funct. Anal. 9 (1) 1 - 7, February 2018. https://doi.org/10.1215/20088752-2017-0018

Information

Received: 2 December 2016; Accepted: 9 January 2017; Published: February 2018
First available in Project Euclid: 29 June 2017

zbMATH: 1382.41019
MathSciNet: MR3758738
Digital Object Identifier: 10.1215/20088752-2017-0018

Subjects:
Primary: 41A36
Secondary: 41A30

Keywords: algebra of complex functions , convergence , Korovkin-type theorems , ‎positive operators

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 1 • February 2018
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