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POINTWISE CONVERGENCE AND SEMIGROUPS ACTING ON VECTOR-VALUED FUNCTIONS
Published online by Cambridge University Press: 22 March 2011
Abstract
A submarkovian C0 semigroup (Tt)t∈ℝ+ acting on the scale of complex-valued functions Lp(X,ℂ) extends to a semigroup of operators on the scale of vector-valued function spaces Lp(X,E), when E is a Banach space. It is known that, if f∈Lp(X,ℂ), where 1<p<∞, then Ttf→f pointwise almost everywhere. We show that the same holds when f∈Lp(X,E) .
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- Research Article
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- Copyright
- Copyright © Australian Mathematical Publishing Association Inc. 2011
Footnotes
It is a pleasure for the first-named author to acknowledge the generous support of an Alexander von Humboldt Foundation Research Prize, and the hospitality of the University of Heidelberg.
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