Closed range multipliers (Q549560)

The main result of the paper is the following: Let \(K\) be a locally compact abelian group and let \(T\) be a Fourier multiplier operator of \(L^2(G)\) such that \(T(L^2)\) is closed. Then \(L^2(G)=\) \(T(L^2) \oplus \operatorname{Ker} T\) and \(T\) is the product of an idempotent and an invertible multiplier operator.