Abstract
Let G be a locally compact abelian group, let μ be a bounded complex-valued Borel measure on G, and let T μ be the corresponding convolution operator on L 1( G). Let X be a Banach space and let S be a continuous linear operator on X. Then we show that every linear operator Φ: X→ L 1( G) such that Φ S= T μ Φ is continuous if and only if the pair ( S, T μ ) has no critical eigenvalue.
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