Perturbation results for exponentially dichotomous operators on general Banach spaces

Journal of Functional Analysis

Volumn 210, Issue 1, 2004, Pages 193-213

  Ran, André C M ^a   van der Mee, Cornelis ^b  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

^b UNIVERSITY OF CAGLIARI   (Italy)

Author keywords

Block operator; Exponential dichotomy; Riccati equation; Semigroup perturbation

Indexed keywords

EID: 1942435476     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2003.07.008     Document Type: Article

References (22)

1. H. Bart, I. Gohberg, M.A. Kaashoek, Minimal Factorization of Matrix and Operator Functions, Operator Theory, Vol. 1, Birkhäuser, Basel and Boston, 1979.
2. H. Bart, I. Gohberg, M.A. Kaashoek, Wiener-Hopf factorization, inverse Fourier transforms and exponentially dichotomous operators, J. Funct. Anal. 68 (1986) 1- 42.
3. H. Bart, I. Gohberg, M.A. Kaashoek, Wiener Hopf equations with symbols analytic in a strip, in: I. Gohberg, M.A. Kaashoek (Eds.), Constructive Methods of Wiener Hopf Factorization, Operator Theory, Vol. 21, Birkhäuser, Basel, 1986, pp. 39-74.
4. S. Bittanti, A.J. Laub, J.C. Willems (Eds.), The Algebraic Riccati Equation, Springer, Berlin, 1991.
5. S. Bochner, R.S. Phillips, Absolutely convergent Fourier expansions for non-commutative normed rings, Ann. Math. 43 (1942) 409-418.
6. R.F. Curtain, H. Zwart, An Introduction to Infinite-dimensional Linear Systems Theory, Springer, New York, 1995.
7. J. Diestel, J.J. Uhl Jr., in: Vector Measures, Mathematical Surveys, Vol. 15, Amer. Math. Soc., Providence, RI, 1977.
8. K.-J. Engel, R. Nagel, in: One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, Vol. 194, Springer, Berlin, 2000.
9. I.A. Feldman, On Wiener Hopf equations with weakly integrable operator kernels, Matem. Issled. 8 (4) (1973) 101-110 [in Russian].
10. I.C. Gohberg, I.A. Feldman, in: Convolution Equations and Projection Methods for their Solution, Translation of Mathematical Monographs, Vol. 41, Amer. Math. Soc., Providence, RI, 1974.
11. I. Gohberg, S. Goldberg, M.A. Kaashoek, Classes of Linear Operators, I, Operator Theory, Vol. 49, Birkhäuser, Basel and Boston, 1990.
12. I.C. Gohberg, J. Leiterer, Factorization of operator functions with respect to a contour. II. Canonical factorization of operator functions close to the identity, Math. Nachrichten 54 (1972) 41-74 [in Russian].
13. W. Greenberg, C.V.M. van der Mee, V. Protopopescu, in: Boundary Value Problems in Abstract Kinetic Theory, Operator Theory, Vol. 23, Birkhäuser, Basel and Boston, 1987.
14. V. Ionescu, M. Weiss, C. Oara, Generalized Riccati Theory and Robust Control. A Popov Function Approach, Wiley, Chichester, 1999.
15. M.A. Kaashoek, C.V.M. van der Mee, A.C.M. Ran, Wiener-Hopf factorization of transfer functions of extended Pritchard-Salamon realizations, Math. Nachrichten 196 (1998) 71-102.
16. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1995.
17. P. Lancaster, L. Rodman, Algebraic Riccati Equations, Oxford University Press, New York, 1995.
18. H. Langer, A.C.M. Ran, B.A. van de Rotten, Invariant subspaces of infinite dimensional Hamiltonians and solutions of the corresponding Riccati equations, in: I. Gohberg, H. Langer (Eds.), Linear Operators and Matrices, Operator Theory, Vol. 130, Birkháuser, Basel and Boston, 2001, pp. 235-254.
19. H. Langer, C. Tretter, Spectral decomposition of some nonselfadjoint block operator matrices, J. Operator Theory 39 (1998) 339-359.
20. H. Langer, C. Tretter, Diagonalization of certain block operator matrices and applications to Dirac operators, in: H. Bart, I. Gohberg, A.C.M. Ran (Eds.), Operator Theory and Analysis, Operator Theory, Vol. 122, Birkhäuser, Basel and Boston, 2001, pp. 331-358.
21. p-spaces, Integral Equations and Operator Theory 6 (1983) 405-443.
22. A.J. Pritchard, D. Salamon, The linear quadratic optimal control problem for infinite-dimensional systems with unbounded input and output operators, SIAM J. Control and Optim. 25 (1987) 121-144.