Ivan Todorov, Queens University Belfast
“Norms of vector functionals”
In this talk, based on a joint work with M. Anoussis, I will discuss the question of when, and how, the norm of a vector functional on an operator algebra can be controlled by the invariant subspace lattice of the algebra. I will introduce a related operator algebraic property and show that it is satisfied by all von Neumann algebras and by all CSL algebras. I will exhibit examples of operator algebras that do not enjoy the property, as a consequence of a characterisation of the weakly closed operator algebras with two non-trivial invariant subspaces that satisfy a scaled version of it.