On geometric structure of symmetric spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:430

Article

Ciesielski, Maciej

关键词: Lorentz spaces;    Symmetric spaces;    Local uniform rotundity;    Strict K-monotonicity;   

DOI  :  10.1016/j.jmaa.2015.04.040

来源: Elsevier

【 摘 要 】

In this article we discuss local approach to strict K-monotonicity and local uniform rotundity in symmetric spaces. We prove several general results on local structure of symmetric spaces E showing relation between strict monotonicity and strict K-monotonicity and the Kadec-Klee property for global convergence in measure. We also present the full criteria for points of upper K-monotonicity in Lorentz spaces Gamma(p,w) for degenerated weight function w. Next we characterize local uniform rotundity in symmetric spaces E proving several correspondences between x is an element of E a point of local uniform rotundity and its decreasing rearrangement x* and absolute value vertical bar x vertical bar. Finally, we apply these results to find complete criteria for local uniform rotundity of Lorentz spaces Gamma(p,w). (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free