Primary summand functions on three-dimensional compact solvmanifolds

Pfeffer, Carolyn

doi:10.1090/S0002-9939-1992-1112499-1

Primary summand functions on three-dimensional compact solvmanifolds
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Proc. Amer. Math. Soc. 116 (1992), 213-217 Request permission

Abstract:

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

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Flows on homogeneous spaces

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