On the structure of spaces of uniformly convergent Fourier series

We first give some new examples of translation invariant subspaces of C or U without local unconditional structure. In the second part, we prove that U and U ⁺ do not have the Gordon–Lewis property. In the third part, we show that absolutely summing operators from U to a K-convex space are compact. As a consequence, U and U ⁺ are not isomorphic. At last, we prove that U and U ⁺ do not have the Daugavet property.