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 ω (i.e.the spectrum of A is contained in a sector of angle 2ω, symmetric about the real positive axis, and is bounded outside every larger sector), then A has a bounded functional calculus in the real interpolation spaces between X and the intersection of the domain and the range of the operator itself.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-1-5,
author = {Giovanni Dore},
title = {$H^{$\infty$}$ functional calculus in real interpolation spaces, II},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {75-83},
zbl = {0985.47015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-1-5}
}
Giovanni Dore. $H^{∞}$ functional calculus in real interpolation spaces, II. Studia Mathematica, Tome 147 (2001) pp. 75-83. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-1-5/