Alexey I. Popov

Abelian, amenable operator algebras are similar to

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

C^{*}

\varrho: A \to B(H_\varrho)

-algebras

of A on a Hilbert space

Semigroups of partial isometries

H_\varrho

Commutators of small rank and reducibility of operator semigroups

, every invariant subspace of

The 2-concavification of a Banach lattice equals the diagonal of the Fremlin tensor square

\varrho(A)

Every operator has almost-invariant subspaces

is topologically complemented by another invariant subspace of

On almost-invariant subspaces and approximate commutation

\varrho(A)

Norm closed operator ideals in Lorentz sequence spaces

, then A is similar to an abelian

Almost Invariant Half-Spaces of Operators on Banach Spaces

C^*