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Weighted norm estimates and L p -spectral independence of linear operators

Peer C. KunstmannHendrik Vogt — 2007

Colloquium Mathematicae

We investigate the L p -spectrum of linear operators defined consistently on L p ( Ω ) for p₀ ≤ p ≤ p₁, where (Ω,μ) is an arbitrary σ-finite measure space and 1 ≤ p₀ < p₁ ≤ ∞. We prove p-independence of the L p -spectrum assuming weighted norm estimates. The assumptions are formulated in terms of a measurable semi-metric d on (Ω,μ); the balls with respect to this semi-metric are required to satisfy a subexponential volume growth condition. We show how previous results on L p -spectral independence can be treated...

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