摘要
We prove that every bounded linear operator on Lp?Lp(R'),s≥1 and 1≤p<∞, that commutes with both the spatial shift operator and the phase shift operator must be a constant multiple of the identity. We also apply this result to identify analysis-synthesis dual Lq-Lp paris and to characterize bi-orthogonal unconditional bases of Lq-Lp, where p?1+q?1=1.
We prove that every bounded linear operator on Lp?Lp(R'),s≥1 and 1≤p<∞, that commutes with both the spatial shift operator and the phase shift operator must be a constant multiple of the identity. We also apply this result to identify analysis-synthesis dual Lq-Lp paris and to characterize bi-orthogonal unconditional bases of Lq-Lp, where p?1+q?1=1.
