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arXiv · 0711.1006

Continuous extension of a densely parameterized semigroup

Eliahu Levy·Orr Shalit
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Abstract

Let S be a dense sub-semigroup of the positive real numbers, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over the positive real numbers. We obtain similar results for non-linear, non-expansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which are extendable to semigroups over the positive real numbers.

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Eliahu Levy, Orr Shalit. 2008-02-13. Continuous extension of a densely parameterized semigroup. https://doi.org/10.1007/s00233-008-9093-1

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