$H^{\infty} $ functional calculus in real interpolation spaces, II
Volume 145 / 2001
Studia Mathematica 145 (2001), 75-83
MSC: 47A60, 46B70.
DOI: 10.4064/sm145-1-5
Abstract
Let $A$ be a linear closed one-to-one operator in a complex Banach space $X$, having dense domain and dense range. If $A$ is of type $\omega $ (i.e.the spectrum of $A$ is contained in a sector of angle $2\omega $, symmetric about the real positive axis, and $\| \lambda (\lambda I - A)^{-1}\| $ is bounded outside every larger sector), then $A$ has a bounded $H^\infty $ functional calculus in the real interpolation spaces between $X$ and the intersection of the domain and the range of the operator itself.
