Annals of Functional Analysis

Convergence properties of nets of operators

Fadel Nasaireh, Dorian Popa, and Ioan Rasa

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afa/1498723218

Digital Object Identifier
doi:10.1215/20088752-2017-0018

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

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

Citation

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. https://projecteuclid.org/euclid.afa/1498723218


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