Let Z denote the additive group of integers. Let H be the Hilbert space of all square summable complex valued functions on Z. Then Z acts unitarily on H by translations. The space C of all compactly supported functions is stable under this action. My question is: does C have a Z-stable complementary space W in H? In other words, is there a Z-stable linear subspace W of H such that H is the direct sum of C and W? Anton