×

On the boundary spectrum of dominated \(C_ 0\)-semigroups. (English) Zbl 0686.47035

Given two one-parameter semigroups S(t) and T(t) in a Banach lattice E the author discusses the relation between dominance, i.e. \[ | S(t)f| \leq T(f)| f|,\quad f\in E,\quad t\geq 0, \] and the boundary spectrum of the respective generators A and B.
Reviewer: J.de Graaf

MSC:

47D03 Groups and semigroups of linear operators
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Arendt, W.,Kato’s inequality, a characterization of generators of positive semigroups, Proc. Royal Irish Acad. Sect. A84 (1984), 155–174. · Zbl 0617.47028
[2] Becker, I., and G. Greiner,On the modulus of one-parameter semigroups, Semigroup Forum34 (1986), 185–201. · Zbl 0635.47036 · doi:10.1007/BF02573162
[3] Caselles, V.,On the peripherical spectrum of positive operators, Israel J. Math.58 (1987), 145–160. · Zbl 0643.47002 · doi:10.1007/BF02785673
[4] Goldstein, G., ”Semigroups of Linear Operators and Applications,” New York, Oxford University Press, 1984. · Zbl 0547.47023
[5] Greiner, G.,Zur Perron-Frobenius Theory stark stetiger Halbgruppen, Math. Z.177 (1981), 401–423. · Zbl 0461.47016 · doi:10.1007/BF01162072
[6] Kerscher, W., and R. Nagel,Positivity and stability for Cauchy problem with delay, Semesterbericht Funktionalanalysis, Tübingen, Sommersemester 1986, 35–54.
[7] Moustakas, U.,Majorisierung und Spektraleigenschaften positiver Operatoren auf Banachverbänden, Dissertation, Universität Tübingen, 1984. · Zbl 0591.47027
[8] Nagel, R. (ed.), One-parameter Semigroups of Positive, Operators, Lect. Notes in Math.1184 Springer-Verlag, 1986.
[9] de Pagter, B., and A. R. Schep,Measures of Non-compactness of Operators in Banach Lattices, J. Funct. Anal.78 (1988), 31–55. · Zbl 0651.47023 · doi:10.1016/0022-1236(88)90131-0
[10] Schaefer, H. H., ”Banach Lattices and Positive Operators”, Springer-Verlag, Berlin-Heidelberg-New York, 1974. · Zbl 0296.47023
[11] Scheffold, E.,Das Spektrum von Verbandsoperatoren in Banachverbänden, Math. Z.123 (1971), 177–190. · Zbl 0216.42101 · doi:10.1007/BF01110116
[12] Schep, A. R.,Weak Kato-inequalities and positive semigroups, Math. Z.190 (1985), 305–314. · Zbl 0609.47050 · doi:10.1007/BF01215132
[13] Webb, G. F.,An operator-theoretic formulation of asynchronous exponential growth, Trans. Amer. Math. Soc.303 (1987), 751–763. · Zbl 0654.47021 · doi:10.1090/S0002-9947-1987-0902796-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.