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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Convolution operators of weak type $ (2,\,2)$ which are not of strong type $ (2,\,2)$


Author: Ryszard Szwarc
Journal: Proc. Amer. Math. Soc. 87 (1983), 695-698
MSC: Primary 43A22
MathSciNet review: 687644
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Abstract: It is well known that if $ G$ is a locally compact and amenable group then the Banach spaces of operators of weak type $ (2,2)$ and of strong type $ (2,2)$ commuting with the right translations on $ G$ are the same. In contrast we show that if $ G$ is a nonabelian free group then there exists an operator of weak type $ (2,2)$ commuting with the right translations on $ G$ which is not of strong type $ (2,2)$.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0687644-7
Keywords: Free group, convolution operator, strong type, weak type
Article copyright: © Copyright 1983 American Mathematical Society