Continuity of Operators Intertwining with Convolution Operators |
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Authors: | C AparicioAR Villena |
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Affiliation: | Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granadaty, Spainf1camilo@ugr.esf1f2avillena@ugr.esf2 |
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Abstract: | Let G be a locally compact abelian group, let μ be a bounded complex-valued Borel measure on G, and let Tμ be the corresponding convolution operator on L1(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→L1(G) such that ΦS=TμΦ is continuous if and only if the pair (S,Tμ) has no critical eigenvalue. |
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Keywords: | automatic continuity intertwining operators multipliers |
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