This is an announcement for the paper “Lower and upper local uniform $K$-monotonicity in symmetric spaces” by Maciej Ciesielskihttps://arxiv.org/find/math/1/au:+Ciesielski_M/0/1/0/all/0/1.

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 $E$.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1707.02632