A pointwise abelian Ergodic theorem for Lp semigroups, 1 ⩽ p < ∞ |
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Authors: | SA McGrath |
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Institution: | Mathematics Department, U.S. Naval Academy, Annapolis, Maryland 21402 USA |
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Abstract: | Let (X, ∑, μ) be a σ-finite measure space and Lp(μ) = Lp(X, ∑, μ), 1 ? p ? ∞, the usual Banach spaces of complex-valued functions. Let {Tt: t ? 0} be a strongly continuous semigroup of positive Lp(μ) operators for some 1 ? p < ∞. Denote by Rλ the resolvent of {Tt}. We show that f?Lp(μ) implies λRλf(x) → f(x) a.e. as λ → ∞. |
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