Summary: Let \(\sigma\) and \(\tau\) be representations of a locally compact abelian group \(G\) on complex Banach spaces \(X\) and \(Y\), respectively. This paper is devoted to study whether every continuous linear operator \(A : X \to Y\) with the property that sp\((\tau,Ax) \subset\text{sp}(\sigma,x)\) \((x \in X)\) intertwines \(\sigma\) and \(\tau\). We are also concerned with those operators satisfying the shrinking property only approximately.