Operators with an absolute functional calculus

被引：0
作者：
N. J. Kalton
T. Kucherenko
机构：
[1] University of Missouri–Columbia,Department of Mathematics
[2] University of California–Los Angeles,Department of Mathematics
来源：
Mathematische Annalen | 2010年 / 346卷
关键词：
Banach Space; Besov Space; Mild Solution; Closed Operator; Functional Calculus;
D O I：
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学科分类号：
摘要：
We study sectorial operators with a special type of functional calculus, which we term an absolute functional calculus. A typical example of such an operator is an invertible operator A (defined on a Banach space X) considered on the real interpolation space (Dom(A), X)θ,p where 0 < θ < 1 and 1 < p < ∞. In general the absolute functional calculus can be characterized in terms of real interpolation spaces. We show that operators of this type have a strong form of the H∞-calculus and behave very well with respect to the joint functional calculus. We give applications of these results to recent work of Arendt, Batty and Bu on the existence of Hölder-continuous solutions for the abstract Cauchy problem.
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页码：259 / 306
页数：47
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