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Keywords:
domination of semigroups; ordered Banach spaces; quasimonotonicity
domination of semigroups; ordered Banach spaces; quasimonotonicity
Summary:
We give criteria for domination of strongly continuous semigroups in ordered Banach spaces that are not necessarily lattices, and thus obtain generalizations of certain results known in the lattice case. We give applications to semigroups generated by differential operators in function spaces which are not lattices.
References:
[1] Herzog G., Kunstmann P.C.: Stability for families of positive semigroups and partial differential equations via one-sided estimates. Demonstratio Math. 34 77-82 (2001). MR 1823086 | Zbl 1084.47512
[2] Kühnemund F., Wacker M.: The Lie-Trotter product formula does not hold for arbitrary sums of generators. Semigroup Forum 60 478-485 (2000). MR 1828831
[3] Lemmert R., Volkmann P.: On the positivity of semigroups of operators. Comment. Math. Univ. Carolinae 39 483-489 (1998). MR 1666770 | Zbl 0970.47026
[4] Martin R.: Nonlinear operators and differential equations in Banach spaces. Pure and Applied Mathematics, John Wiley and Sons, New York-London-Sydney, 1976. MR 0492671 | Zbl 0333.47023
[5] Nagel R. (Ed.): One-parameter semigroups of positive operators. Lecture Notes in Mathematics 1184, Springer, Berlin, 1986. MR 0839450 | Zbl 0643.92017
[6] Ouhabaz E.M.: Invariance of closed convex sets and domination criteria for semigroups. Potential Anal. 5 611-625 (1996). MR 1437587 | Zbl 0868.47029
[7] Stein M., Voigt J.: The modulus of matrix semigroups. Arch. Math. (Basel) 82 311-316 (2004). MR 2057381 | Zbl 1070.47034
[8] Volkmann P.: Gewöhnliche Differentialungleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorräumen. Math. Z. 127 (1972), 157-164. MR 0308547 | Zbl 0226.34058
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