Laurent W. Marcoux

Weak amenability of triangular Banach algebras

Let A and B be unital Banach algebras, and let M be a Banach A, B-module. Then T = [ A M 0 B ] becomes a triangular Banach algebra when equipped with the Banach space norm || [ a m 0 b ] || = ||a|| A +||m|| M + ||b|| B . A Banach algebra T is said to be n-weakly amenable if all derivations from T into its n th dual space T (n) are inner. In this paper we investigate Arens regularity and n-weak amenability of a triangular Banach algebra T in relation to that of the algebras A, B and their action on the module M.

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

Relative annihilators and relative commutants in non-selfadjoint operator algebras

H_\varrho

An approximate, multivariable version of Specht's theorem

, every invariant subspace of

A spatial version of Wedderburn’s Principal Theorem

\varrho(A)

On the topological stable rank of non-selfadjoint operator algebras

is topologically complemented by another invariant subspace of

Transitive Spaces of Operators

\varrho(A)

On almost-invariant subspaces and approximate commutation

, then A is similar to an abelian