Two points, one limit: Homogenization techniques for two-point local algebras

We study several algebras generated by convolution, multiplication and flip operators on L p ( R ) , their Calkin counterparts and derive new isomorphism relations. We introduce a new class of homogenization strong limits, compatible with the flip operator and which explore the properties of the Fourier transform in L p ( R ) , when p ≠ 2 .