Interpolation of Banach algebras and tensor products of Banach couples

Using tensor products of Banach couples we study a class of interpolation functors with the property that to every Banach couple of Banach algebras they give an interpolation space which is a Banach algebra. For the real θ, 1-method we give a complete answer to the question of when the interpolation space is unital.  2003 Elsevier Science (USA). All rights reserved