For 0<θ<1, (M(𝕋), c0(ℤ))_θ equals (L^1(𝕋), c0(ℤ))_θ, and a constructed operator U_θ maps the Garling-Smith interpolation spaces with the symmetry C_{θ,p} ≅ C_{1-θ,p}.
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Two remarks on the interpolation space
For 0<θ<1, (M(𝕋), c0(ℤ))_θ equals (L^1(𝕋), c0(ℤ))_θ, and a constructed operator U_θ maps the Garling-Smith interpolation spaces with the symmetry C_{θ,p} ≅ C_{1-θ,p}.