Almost transitivity of some function spaces


The almost transitive norm problem is studied for Lp(μ, X), C(K,X) and for certain Orlicz and Musielak-Orlicz spaces. For example if p ≠ 2 < ∞ then Lp(μ) has almost transitive norm if and only if the measure μ is homogeneous. It is shown that the only Musielak-Orlicz space with almost transitive norm is the L^-space. Furthermore, an Orlicz space has an almost transitive norm if and only if the norm is maximal. Lp(μ, X) has almost transitive norm if Lp(μ)) and X have. Separable spaces with nontrivial Lp-structure fail to have transitive norms. Spaces with nontrivial centralizers and extreme points in the unit ball also fail to have almost transitive norms. © 1994, Cambridge Philosophical Society. All rights reserved.

Publication Title

Mathematical Proceedings of the Cambridge Philosophical Society