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Abelian, amenable operator algebras are similar to C*-algebras
Suppose that H is a complex Hilbert space and that B(H) denotes the bounded
linear operators on H. We show that every abelian, amenable operator algebra is
similar to a C*-algebra. We do this by showing that if A is an abelian
subalgebra of B(H) with the property that given any bounded representation
of A on a Hilbert space , every
invariant subspace of is topologically complemented by another
invariant subspace of , then A is similar to an abelian
-algebra
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