Characteristics for certain classes of Banach spaces and their applications (Q1099392)

Let E be a Banach ideal and \(G=(g_ t)\) a semigroup of linear operators acting on E. Let also \(\tau\vdash K(\tau)\) be a kernel. Sufficient conditions are given so that the family of integral operators \[ (T_ G^{\lambda}f(t)=2\lambda \int^{\infty}_{0}G_{\tau}f(t)\times K(\tau \lambda)d\tau) \] should converge (pointwise) to the identity as \(\lambda\) tends to infinity.