CMA Research Report

MRR02-005

Similarities of ω-accretive operators

Abstract:  Given a number 0<ω ≤ π/2, an ω-accretive operator is a sectorial operator A on Hilbert space whose numerical range lies in the closed sector of all z ∈ C such that |Arg(z)| \leq ω. It is easy to check that any such operator admits bounded imaginary powers, with |A^it| ≤ e^{ω |t|} for any real number t. We show that conversely, A is similar to an ω-accretive operator if |A^it| ≤ e^{ω |t|} for any t ∈ R.

AMS Classification:  47A60
Date:  22 February 2002

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