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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  L   p  ‐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.

A crossed product approach to Orlicz spaces