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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Primary summand functions on three-dimensional compact solvmanifolds


Author: Carolyn Pfeffer
Journal: Proc. Amer. Math. Soc. 116 (1992), 213-217
MSC: Primary 22E25; Secondary 22E40
MathSciNet review: 1112499
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1112499-1
PII: S 0002-9939(1992)1112499-1
Article copyright: © Copyright 1992 American Mathematical Society