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arXiv · 1707.02632

Lower and upper local uniform $K$-monotonicity in symmetric spaces

Maciej Ciesielski
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Abstract

Using the local approach to the global structure of a symmetric space $E$ we establish a relationship between strict $K$- monotonicity, lower (resp. upper) local uniform $K$-monotonicity, order continuity and the Kadec-Klee property for global convergence in measure. We also answer the question under which condition upper local uniform $K$-monotonicity concludes upper local uniform monotonicity. Finally, we present a correlation between $K$-order continuity and lower local uniform $K$-monotonicity in a symmetric space $E$ under some additional assumptions on $E$.

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Maciej Ciesielski. 2017-07-09. Lower and upper local uniform $K$-monotonicity in symmetric spaces. https://doi.org/10.1215/17358787-2017-0047

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