Characterizations of Kadec-Klee properties in symmetric spaces of measurable functions

Abstract

We present several characterizations of Kadec-Klee properties in symmetric function spaces on the half-line, based on the K K -functional of J. Peetre. In addition to the usual Kadec-Klee property, we study those symmetric spaces for which sequential convergence in measure (respectively, local convergence in measure) on the unit sphere coincides with norm convergence.