Strongly amenable involutive representations of involutive Banach algebras

摘要

Let A be a Banach ?-algebra and let ? be a nonzero self-adjoint character on A. For a ?-representation π of A on a Hilbert space H, we introduce and study strong ?-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.