On the Takai duality for $$L^{p}$$ operator crossed products

Abstract

This paper aims to study the L p Takai duality problem raised by N. C. Phillips. Let G be a countable discrete Abelian group, A be a separable unital L p operator algebra with p ∈ [1, ∞), and α be an isometric action of G on A. When A is pincompressible and has unique L p operator matrix norms, it is proved in this paper that the iterated L p operator crossed product