Banach space operators with a bounded H∞ functional calculus

Journal of the Australian Mathematical Society

Michael Cowling¹ 

[1] Ian Doust

关键词: 47A60;   

DOI  :  10.1017/S1446788700037393

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

In this paper, we give a general definition for f(T) when T is a linear operator acting in a Banach space, whose spectrum lies within some sector, and which satisfies certain resolvent bounds, and when f is holomorphic on a larger sector.We also examine how certain properties of this functional calculus, such as the existence of a bounded H∈ functional calculus, bounds on the imaginary powers, and square function estimates are related. In particular we show that, if T is acting in a reflexive Lp space, then T has a bounded H∈ functional calculus if and only if both T and its dual satisfy square function estimates. Examples are given to show that some of the theorems that hold for operators in a Hilbert space do not extend to the general Banach space setting.

【 授权许可】

Unknown