# Majorization of ${C}_{0}$-semigroups in ordered Banach spaces

Gerd Herzog; Peer Christian Kunstmann

Commentationes Mathematicae Universitatis Carolinae (2006)

- Volume: 47, Issue: 1, page 47-54
- ISSN: 0010-2628

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topHerzog, Gerd, and Kunstmann, Peer Christian. "Majorization of $C_0$-semigroups in ordered Banach spaces." Commentationes Mathematicae Universitatis Carolinae 47.1 (2006): 47-54. <http://eudml.org/doc/249877>.

@article{Herzog2006,

abstract = {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.},

author = {Herzog, Gerd, Kunstmann, Peer Christian},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {domination of semigroups; ordered Banach spaces; quasimonotonicity; domination of semigroups; ordered Banach spaces; quasimonotonicity},

language = {eng},

number = {1},

pages = {47-54},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Majorization of $C_0$-semigroups in ordered Banach spaces},

url = {http://eudml.org/doc/249877},

volume = {47},

year = {2006},

}

TY - JOUR

AU - Herzog, Gerd

AU - Kunstmann, Peer Christian

TI - Majorization of $C_0$-semigroups in ordered Banach spaces

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2006

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 47

IS - 1

SP - 47

EP - 54

AB - 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.

LA - eng

KW - domination of semigroups; ordered Banach spaces; quasimonotonicity; domination of semigroups; ordered Banach spaces; quasimonotonicity

UR - http://eudml.org/doc/249877

ER -

## References

top- 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). (2001) Zbl1084.47512MR1823086
- Kühnemund F., Wacker M., The Lie-Trotter product formula does not hold for arbitrary sums of generators, Semigroup Forum 60 478-485 (2000). (2000) MR1828831
- Lemmert R., Volkmann P., On the positivity of semigroups of operators, Comment. Math. Univ. Carolinae 39 483-489 (1998). (1998) Zbl0970.47026MR1666770
- Martin R., Nonlinear operators and differential equations in Banach spaces, Pure and Applied Mathematics, John Wiley and Sons, New York-London-Sydney, 1976. Zbl0333.47023MR0492671
- Nagel R. (Ed.), One-parameter semigroups of positive operators, Lecture Notes in Mathematics 1184, Springer, Berlin, 1986. Zbl0643.92017MR0839450
- Ouhabaz E.M., Invariance of closed convex sets and domination criteria for semigroups, Potential Anal. 5 611-625 (1996). (1996) Zbl0868.47029MR1437587
- Stein M., Voigt J., The modulus of matrix semigroups, Arch. Math. (Basel) 82 311-316 (2004). (2004) Zbl1070.47034MR2057381
- Volkmann P., Gewöhnliche Differentialungleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorräumen, Math. Z. 127 (1972), 157-164. (1972) Zbl0226.34058MR0308547

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