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Sums of commuting operators with maximal regularity

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Le Merdy C., Simard A.

Studia Mathematica

2001

tom 147

nr 2

103-118

Let Y be a Banach space and let $S ⊂ L_{p}$ be a subspace of an $L_{p}$ space, for some p ∈ (1,∞). We consider two operators B and C acting on S and Y respectively and satisfying the so-called maximal regularity property. Let ℬ and 𝓒 be their natural extensions to $S(Y) ⊂ L_{p}(Y)$. We investigate conditions that imply that ℬ + 𝓒 is closed and has the maximal regularity property. Extending theorems of Lamberton and Weis, we show in particular that this holds if Y is a UMD Banach lattice and $e^{-tB}$ is a positive contraction on $L_{p}$ for any t ≥ 0.

Ograniczanie wyników

1 Studia Mathematica

1 Le Merdy C.

1 Simard A.

1 2001

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Sums of commuting operators with maximal regularity