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/