Strict K-monotonicity and K-order continuity in symmetric spaces

2017/05/17 by Maciej Ciesielski, Ciesielski, Maciej
Mathematics · #46B20 #46B42 #46E30 #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.1705.06062

openalex publication_date 2017/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to strict K- monotonicity and K-order continuity in symmetric spaces. Using the local approach to the geometric structure in a symmetric space E we investigate a connection between strict K-monotonicity and global convergence in measure of a sequence of the maximal functions. Next, we solve an essential problem whether an existence of a point of K-order continuity in a symmetric space E on [0,∞) implies that the embedding E\hookrightarrowL¹[0,∞) does not hold. We finish this article with a complete characterization of K-order continuity in a symmetric space E that is written using a notion of order continuity under some assumptions on the fundamental function of E.

Citations

• Strictly and uniformly monotone Musielak-Orlicz spaces and applications to best approximation

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