Abstract

Let A be a Banach ∗ -algebra and let φ be a nonzero self-adjoint character on A . For a   ∗ -representation π of A on a Hilbert space H , we introduce and study strong φ -amenability of π in terms of certain states on the von Neumann algebra of bounded operators on H . We then give some characterizations of this notion in terms of certain positive functionals on A . We finally investigate some hereditary properties of strong φ -amenability of Banach algebras.

AMSC: Primary 43A07, 46K05, 46K10, Secondary 47B65.