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

 

Complemented subspaces and amenability: a counterexample


Author: Yuji Takahashi
Journal: Proc. Amer. Math. Soc. 118 (1993), 1113-1115
MSC: Primary 43A07; Secondary 43A15
MathSciNet review: 1143024
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Abstract: We give an example of a left amenable discrete semigroup $ S$ such that $ {l^\infty }(S)$ has weak$ ^{{\ast}}$-closed selfadjoint left translation invariant subalgebras that are weak$ ^{{\ast}}$-complemented but not invariantly complemented in $ {l^\infty }(S)$. This resolves negatively a problem raised by Lau.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1143024-8
PII: S 0002-9939(1993)1143024-8
Keywords: Left amenable semigroup, complemented subspace, invariantly complemented subspace, weak$ ^{{\ast}}$-complemented subspace
Article copyright: © Copyright 1993 American Mathematical Society