Uniqueness of pre-generators on the dual of a Banach space
by
Ludovic Dan Lemle
University Lyon1, France

Let (X, ∥ . ∥) be a Banach space. In general, for a C₀-semigroup {T(t)}_{t ≥ 0} on (X, ∥ . ∥), its adjoint semigroup {T^*(t)}_{t ≥ 0} is no longer strongly continuous on the dual space (X^*, ∥ . ∥^*). Consider on X^* the topology of uniform convergence on compact subsets of (X, ∥ . ∥) denoted by C(X^*, X), for which the usual semigroups in literature becomes C₀-semigroups.
A linear operator A:D→X^* with domain D dense in (X^*, C(X^*, X)) is said to be a pre-generator in (X^*, C(X^*, X)), if there exists some C₀-semigroup on (X^*, C(X^*, X)) such that its generator extends A.

The main purpose of this talk is to prove that there is only one C₀-semigroup {T(t)}_{t ≥ 0} on (X^*, C(X^*, X)) such that is generator L extends A if and only if D is a core of L.

Date received: May 16, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawh-48.