Continuous extension of a densely parameterized semigroup

Details Continuous extension of a densely parameterized semigroup Continuous extension of a densely parameterized semigroup

2007-11-07

arxiv.org/abs/0711.1006v2

Semigroup Forum, 78/2 (2009), 276-284

Mathematics

Functional Analysis

8 pages, minor modifications

Scientific paper

10.1007/s00233-008-9093-1

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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