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Let q> G C'[-1,1]. For/G !»(-1, 1) define T«,/(i) = j/(i) + -I-dt. TT J-1 i -/ Our main result says Tq, has invariant subspaces of infinite codimension. Received by the editors November 29, 1971. A MS 1969 subject classifications. Primary 4615, 4710.doi:10.2307/2039476 fatcat:35z2233qfrfx5e5kjp2wkkot4q