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Inverses of generators of nonanalytic semigroups. (English) Zbl 1167.47035
It is well-known that if \(A\) is an injective analytic semigroup on a Banach space \(X\), then \(A^{-1}\) generates an analytic semigroup. This property does not carry over if the analyticity of the semigroup is removed. This paper faces the natural questions arising from this fact, i.e., what one can say in general about the inverse of a generator of uniformly bounded semigroups, what properties ensure that both \(A\) and \(A^{-1}\) generate a uniformly bounded semigroup, and what is the relation between the semigroups generated by \(A\) and by \(A^{-1}\).

MSC:
47D03 Groups and semigroups of linear operators
47A60 Functional calculus for linear operators
47D60 \(C\)-semigroups, regularized semigroups
47D62 Integrated semigroups
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