A Remark on the Norm of Integer Order Favard Spaces
نویسندگان
چکیده
For a generator A of a C0 -semigroup T (·) on a Banach space X we consider the semi-norm Mk x := lim supt→0+ ‖t−1(T (t)− I)Ak−1x‖ on the Favard space Fk of order k associated with A . The use of this semi-norm is motivated by the functional analytic treatment of time-discretization methods of linear evolution equations. We show that sharp inequalities for bounded linear operators on D(Ak) can be extended to the larger space Fk by using the semi-norm Mk (·) . We also show that Mk (·) is a norm equivalent to the norms that are usually considered in the literature if A has a bounded inverse.
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