Abstract
It is well known that if G G is a locally compact and amenable group then the Banach spaces of operators of weak type ( 2 , 2 ) (2,2) and of strong type ( 2 , 2 ) (2,2) commuting with the right translations on G G are the same. In contrast we show that if G G is a nonabelian free group then there exists an operator of weak type ( 2 , 2 ) (2,2) commuting with the right translations on G G which is not of strong type ( 2 , 2 ) (2,2) .
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