On Riccati equation in ordered Banach algebras

• Autorzy: Herzog G. , Lemmert R.
• Języki publikacji: EN

Abstrakty

EN

We consider Riccati differential equations in ordered Banach algebras A, and prove invariance and comparison theorems for the case that the right hand side of a Riccati equation is quasimonotone increasing on the set of quasipositive elements (which are the quasimonotone increasing linear mappings in case that A is the operator algebra of an ordered Banach space).

Słowa kluczowe

EN

Riccati differential equation; ordered Banach algebras; quasimonotonicity

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 4
• Strony: 783--790
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Herzog G.

• Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany

autor

Lemmert R.

• Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany

Bibliografia

• [1] W. A. Coppel, Disconjugacy, Lect. Notes Math. 220, Springer, Berlin, 1971.
• [2] P. Gritzmann, V. Klee, B.-S. Tam, Cross-positive matrices revisited, Linear Algebra Appl. 223/224 (1995), 285-305.
• [3] G. Herzog, R. Lemmert, On quasipositive elements in ordered Banach algebras, Stud. Math. 129 (1998), 59-65.
• [4] D. H. Jacobson, New conditions for boundedness of the solution of a matrix Riccati differential equation, J. Diff. Eq. 8 (1970), 258-263.
• [5] R. Redheffer, On the relation of transmission-line theory to scattering and transfer, J. Math. Phys. 41 (1962), 1-41.
• [6] R. Redheffer, Matrix differential equations, Bull. Amer. Math. Soc. 81 (1975), 485-488.
• [7] R. Redheffer, P. Volkmann, Differential equations in operator algebras II. Invariance of the order cone, J. Diff. Eq. 130 (1996), 356-367.
• [8] W. T. Reid, Riccati Differential Equations, Academic Press, New York, 1972.
• [9] H. Schneider, Positive operators and an inertia theorem, Numerische Math. 7 (1965), 11-17.
• [10] R. J. Stern, Generalized M-matrices, Linear Algebra Appl. 41 (1981), 201-208.
• [11] R. J. Stern, H. Wolkowicz, Exponential nonnegativity on the ice cream cone, SIAM J. Matrix Anal. Appl. 12 (1991), 160-165.
• [12] A. N. Stokes, Differential inequalities and the matrix Riccati equation, Bull. Austral. Math. Soc. 9 (1973), 315-317.
• [13] A. N. Stokes, A special property of the matrix Riccati equation, Bull. Austral. Math. Soc. 10 (1974), 245-253.
• [14] P. Volkmann, Gewöhnliche Differentialungleichungen mit quasimonoton wachsen - den Funktionen in topologischen Vektorräumen, Math. Z. 127 (1972), 157-164.
• [15] P. Volkmann, Über die Invarianz konvexer Mengen und Differentialungleichungen in einem normierten Räume, Math. Ann. 203 (1973), 201-210.