Remarks on Embeddable Semigroups in Groups and a Generalization of Some Cuthbert’s Results
نویسندگان
چکیده
Let (U(t))t≥0 be a C0-semigroup of bounded linear operators on a Banach space X. In this paper, we establish that if, for some t0 > 0, U(t0) is a Fredholm (resp., semiFredholm) operator, then (U(t))t≥0 is a Fredholm (resp., semi-Fredholm) semigroup. Moreover, we give a necessary and sufficient condition guaranteeing that (U(t))t≥0 can be embedded in a C0-group on X. Also we study semigroups which are near the identity in the sense that there exists t0 > 0 such thatU(t0)−I ∈ (X), where (X) is an arbitrary closed two-sided ideal contained in the set of Fredholm perturbations. We close this paper by discussing the case where (X) is replaced by some subsets of the set of polynomially compact perturbations.
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