  In this thesis we explore the the possibility of characterising C* algebras
by their (non-isometric) Banach algebra structure alone.
  We introduce a property of Banach algebras, the Total Reduction Property, and
conjecture that a Banach algebra has this property if and only if it is
isomorphic to a C* algebra. We establish some partial results in support of
this conjecture.

Operator Algebras