Subspaces of $L_p$ with more than one complex structure
Subspaces of $L_p$ with more than one complex structure
We propose a method of constructing explicit Banach spaces not isomorphic to their complex conjugates as subspaces of a natural class of Banach spaces. In particular, it is shown that $L_p$, for $1\leq p<2$, contains real subspaces with at least two non-isomorphic complex structures.