The Banach algebra generated by a -semigroup
The Banach algebra generated by a -semigroup
Let T={T(t)}t⩾0 be a bounded C0-semigroup on a Banach space with generator A. We define AT as the closure with respect to the operator-norm topology of the set {fˆ(T):f∈L1(R+)}, where fˆ(T)=∫0∞f(t)T(t)dt is the Laplace transform of f∈L1(R+) with respect to the semigroup T. Then AT is a commutative Banach algebra. …