Primary summand functions on three-dimensional compact solvmanifolds

Abstract

Leonard Richardson has shown that for a certain class of three-dimensional compact solvmanifolds, projections onto π \pi -primary summands of L 2 ( M ) {L^2}\left ( M \right ) do not preserve the continuity of functions on M M . It is shown here that if the π \pi -primary projection of a continuous function is L ∞ {L^\infty } then it is actually continuous. From this it follows that there are continuous functions on M M whose π \pi -primary projections are essentially unbounded.