Vector-valued invariant means on spaces of bounded operators on Banach algebras

VECTOR-VALUED INVARIANT MEANS ON SPACES OF BOUNDED LINEAR MAPS

MAHSHID DASHTI (Isfahan and Malayer),
RASOUL NASR-ISFAHANI (Isfahan and Tehran) and
SIMA SOLTANI RENANI (Isfahan)

Abstract: Let A be a Banach algebra and let M be a W-algebra. For a homomorphism
 from A into M, we introduce and study M-valued invariant -means on
the space of bounded linear maps from A into M. We establish several characterizations
of existence of an M-valued invariant -mean on B(A; M). We also study the relation
between existence of an M-valued invariant -mean on B(A; M) and amenability of A.
Finally, for a character  of A, we give some descriptions for -amenability of A in terms
of M-valued invariant -means.