Let a real Banach algebra A with unit be ordered by an algebra cone K. We study the elements a ∈ A with exp(ta) ∈ K, t≥ 0.
@article{bwmeta1.element.bwnjournal-article-smv129i1p59bwm,
author = {Gerd Herzog and Roland Lemmert},
title = {On quasipositive elements in ordered Banach algebras},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {59-65},
zbl = {0908.46032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv129i1p59bwm}
}
Herzog, Gerd; Lemmert, Roland. On quasipositive elements in ordered Banach algebras. Studia Mathematica, Tome 129 (1998) pp. 59-65. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv129i1p59bwm/
[00000] [1] G. P. Barker, On matrices having an invariant cone, Czechoslovak Math. J. 22 (1972), 49-68. | Zbl 0238.15005
[00001] [2] F. F. Bonsall, and J.Duncan, Complete Normed Algebras, Springer, 1973. | Zbl 0271.46039
[00002] [3] H.-J. Krieger, Beiträge zur Theorie positiver Operatoren, Akademie-Verlag, Berlin, 1969.
[00003] [4] R. Loewy and H. Schneider, Positive operators on the n-dimensional ice cream cone, J. Math. Anal. Appl. 49 (1975), 375-392. | Zbl 0308.15011
[00004] [5] H. Raubenheimer and D. Rode, Cones in Banach algebras, Indag. Math. 7 (1996), 489-502.
[00005] [6] R. Redheffer and W. Walter, Flow-invariant sets and differential inequalities in normed spaces, Appl. Anal. 5 (1975), 149-161. | Zbl 0353.34067
[00006] [7] H. H. Schaefer, Topological Vector Spaces, Springer, 1980.
[00007] [8] P. Volkmann, Gewöhnliche Differentialungleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorräumen, Math. Z. 127 (1972), 157-164. | Zbl 0226.34058
[00008] [9] P. Volkmann, Über die Invarianz konvexer Mengen und Differentialungleichungen in einem normierten Raume, Math. Ann. 203 (1973), 201-210. | Zbl 0251.34039