Suppose A is a sectorial operator on a Banach space X, which admits an H∞-calculus. We study conditions on a multiplicative perturbation B of A which ensure that B also has an H∞-calculus. We identify a class of bounded operators T : X→X, which we call strongly triangular, such that if B = (1 + T) A is sectorial then it also has an H∞-calculus. In the case X is a Hilbert space an operator is strongly triangular if and only if ∑ Sn(T)/n <∞ where (Sn(T))n=1∞ are the singular values of T.
@article{urn:eudml:doc:42036,
title = {Perturbations of the H$\infty$-calculus},
journal = {Collectanea Mathematica},
volume = {58},
year = {2007},
pages = {291-325},
zbl = {1148.47012},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42036}
}
Kalton, N.J. Perturbations of the H∞-calculus. Collectanea Mathematica, Tome 58 (2007) pp. 291-325. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42036/