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Some remarks concerning the spaces of multipliers and convolutors, \({\mathcal{O}_M}\) and \({\mathcal{O}'_C}\), of Laurent Schwartz

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Abstract

We specify representations of the spaces \({\mathcal{O}_M}\) and \({\mathcal{O}'_M}\) and show that they are not appropriate to conclude that \({\mathcal{O}_M}\) is ultrabornological. We investigate topological properties, multipliers and convolutors of Kučera’s spaces occurring in his proof (Int J Math Math Sci 8(4):813–816, 1985) of the fact that \({\mathcal{O}_M}\) is ultrabornological and show that the proof has a flaw.

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  1. Institut für Mathematik, Universität Innsbruck, Technikerstr. 13, 6020, Innsbruck, Austria

    Julian Larcher

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Larcher, J. Some remarks concerning the spaces of multipliers and convolutors, \({\mathcal{O}_M}\) and \({\mathcal{O}'_C}\), of Laurent Schwartz. RACSAM 106, 407–417 (2012). https://doi.org/10.1007/s13398-012-0059-5

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