For a bounded and sectorial linear operator V in a Banach space, with spectrum in the open unit disc, we study the operator . We show, for example, that Ṽ is sectorial, and asymptotically of type 0. If V has single-point spectrum 0, then Ṽ is of type 0 with a single-point spectrum, and the operator I-Ṽ satisfies the Ritt resolvent condition. These results generalize an example of Lyubich, who studied the case where V is a classical Volterra operator.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-2-1,
author = {Nick Dungey},
title = {On an integral of fractional power operators},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {157-164},
zbl = {1176.47020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-2-1}
}
Nick Dungey. On an integral of fractional power operators. Colloquium Mathematicae, Tome 116 (2009) pp. 157-164. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-2-1/