A characterization of exponentially dichotomic and exponentially stable -semigroups in terms of solutions of an operator equation of Lyapunov type is presented. As a corollary a new and shorter proof of van Neerven’s recent characterization of exponential stability in terms of boundedness of convolutions of a semigroup with almost periodic functions is given.
@article{bwmeta1.element.bwnjournal-article-smv132i2p141bwm,
author = {Ph\'ong V\~u},
title = {On the exponential stability and dichotomy of $C\_0$-semigroups},
journal = {Studia Mathematica},
volume = {133},
year = {1999},
pages = {141-149},
zbl = {0926.47026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv132i2p141bwm}
}
Vũ, Phóng. On the exponential stability and dichotomy of $C_0$-semigroups. Studia Mathematica, Tome 133 (1999) pp. 141-149. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv132i2p141bwm/
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