Boundary values of holomorphic semigroups of unbounded operators and similarity of certain perturbations |
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| Authors: | Rhonda J Hughes Shmuel Kantorovitz |
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| Affiliation: | 1. Tufts University, Medford, Massachusetts 02155, U.S.A.;2. Institute for Independent Study, Radcliffe College, Cambridge, Massachusetts 02138 U.S.A.;3. University of Illinois at Chicago Circle, Chicago, Illinois 60680 U.S.A.;4. Bar-Ilan University, Ramat-Gan, Israel |
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| Abstract: | We obtain sufficient conditions for a “holomorphic” semigroup of unbounded operators to possess a boundary group of bounded operators. The theorem is applied to generalize to unbounded operators results of Kantorovitz about the similarity of certain perturbations. Our theory includes a result of Fisher on the Riemann-Liouville semigroup in Lp(0, ∞) 1 < p < ∞. In this particular case we give also an alternative approach, where the boundary group is obtained as the limit of groups in the weak operator topology. |
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