When is a linear convolution system stabilizable?

Lack of operator closedness and closability arguments are used to discuss the impossibility of finite lp/Lp gain stabilization of unstable finite-dimensional linear (convolution operator) systems in the doubly infinite time-axis case for any 1⩽p⩽∞. The presented analysis generalizes and refines a result due to Georgiou and Smith (IEEE Trans. Automat. Control 40 (1995) 516) for the L2(−∞,∞) setting.