Kadec-Klee properties of some quasi-Banach function spaces
A Banach space \(X\) is said to have the Kadec-Klee property if every sequence \((x_n)_{n\in \mathbb{N}}\) in \(X\) which is weakly convergent to some \(x\in X\) and satisfies \(\|x_n\|\to \|x\|\) is actually norm-convergent to \(x\). This paper concerns Kadec-Klee-type properties with respect to convergence in measure (instead of weak convergence) in quasi-Banach function spaces. Both global and local convergence in measure are considered. In particular, such properties are studied in symmetrizations of quasi-Banach function spaces, in Marcinkiewicz spaces and in Lorentz spaces.
scientific article; zbMATH DE number 6946886
scientific article