Domination properties and extension of positive compact operators on pre-Riesz spaces

2018/09/16 by Onno van Gaans, Feng Zhang, van Gaans, Onno +1
Mathematics · #46B40 #47B60 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1809.05873

openalex publication_date 2018/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper concerns positive domination property of compact operators on pre-Riesz spaces. The method is embedding the pre-Riesz space to the Riesz completion. It extends the order continuous norms in pre-Riesz spaces to Riesz completions. The compactness of third power of a positive operator is obtained in a pre-Riesz space which has an order unit.

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