Complemented Subspaces and Amenability: A Counterexample
Yuji Takahashi · Proceedings of the American Mathematical Society · 1993
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.