Abstract
The goal of this article is to present some method of optimal extension of positive order continuous and \( \sigma \)-order continuous operators on quasi-Banach function spaces with values in Dedekind complete quasi-Banach lattices. The optimal extension of such an operator is the smallest extension of the Bartle–Dunford–Schwartz type integral. It is also shown that if a positive operator sends order convergent sequences to quasinorm convergent sequences, then its optimal extension is the Bartle–Dunford–Schwartz type integral.
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Tasoev, B.B. Optimal Extension of Positive Order Continuous Operators with Values in Quasi-Banach Lattices. Sib Math J 61, 884–894 (2020). https://doi.org/10.1134/S0037446620050122
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DOI: https://doi.org/10.1134/S0037446620050122
Keywords
- quasi-Banach lattice
- optimal extension
- optimal domain
- Bartle–Dunford–Schwartz integration
- weakly integrable functions
- Banach function space