Let A(·) be a regular function defined on a connected metric space G whose values are mutually commuting essentially Kato operators in a Banach space. Then the spaces and do not depend on z ∈ G. This generalizes results of B. Aupetit and J. Zemánek.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-1-5,
author = {K.-H. F\"orster and V. M\"uller},
title = {Stability of infinite ranges and kernels},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {61-73},
zbl = {1093.47013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-1-5}
}
K.-H. Förster; V. Müller. Stability of infinite ranges and kernels. Studia Mathematica, Tome 173 (2006) pp. 61-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-1-5/