Annals of Functional Analysis

Convergence properties of nets of operators

Fadel Nasaireh, Dorian Popa, and Ioan Rasa

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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.

Article information

Ann. Funct. Anal., Volume 9, Number 1 (2018), 1-7.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 41A36: Approximation by positive operators
Secondary: 41A30: Approximation by other special function classes

positive operators algebra of complex functions convergence Korovkin-type theorems


Nasaireh, Fadel; Popa, Dorian; Rasa, Ioan. Convergence properties of nets of operators. Ann. Funct. Anal. 9 (2018), no. 1, 1--7. doi:10.1215/20088752-2017-0018.

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