Completely continuous Banach algebras

For a banach algebra a, we introduce c.c(a), the set of all φ ∈ a ∗ such that θφ : a → a ∗ is a completely continuous operator, where θφ is defined by θφ(a) = a · φ for all a ∈ a. we call a, a completely continuous banach algebra if c.c(a) = a ∗ . we give some examples of completely continuous banach algebras and a sufficient condition for an open problem raised for the first time by j.e gal`e, t.j. ransford and m. c. white: is there exist an infinite dimensional amenable banach algebra whose underlying banach space is reflexive? we prove that a reflexive, amenable, completely continuous banach algebra with the approximation property is trivial.