A crossed product approach to Orlicz spaces

Abstract

We show how the known theory of non-commutative Orlicz spaces for semifinite von Neumann algebras equipped with an faithful normal semifinite trace may be recovered using crossed product techniques. Then using this as a template, we construct analogues of such spaces for type III algebras. The constructed spaces naturally dovetail with and closely mimic the behaviour of Haagerup Lp-spaces.We then define a modified K-method of interpolation which seems to better fit the present context, and give a formal prescription for using this method to define what may be regarded as type III Riesz–Fischer spaces