Factoring weakly compact operators and the inhomogeneous Cauchy problem

Bárcenas, Diómedes

doi:10.1090/S0002-9939-99-05127-8

Factoring weakly compact operators and the inhomogeneous Cauchy problem
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Proc. Amer. Math. Soc. 128 (2000), 1357-1360 Request permission

Abstract:

By using the technique of factoring weakly compact operators through reflexive Banach spaces we prove that a class of ordinary differential equations with Lipschitz continuous perturbations has a strong solution when the problem is governed by a closed linear operator generating a strongly continuous semigroup of compact operators.

References

D. Bárcenas and W. Urbina, Measurable Multifunctions in non separable Banach spaces, SIAM, J. Math. Anal. 28, (1997), 1212-1226.
W. J. Davis, T. Figiel, W. B. Johnson, and A. Pełczyński, Factoring weakly compact operators, J. Functional Analysis 17 (1974), 311–327. MR 0355536, DOI 10.1016/0022-1236(74)90044-5
O. Diekman, S. A. van Gils, S. M. Verduyn Lunel and H. O. Wather, Delay equations: Functional, complex and nonlinear analysis, Springer Verlag, Berlin, 1995.
J. Dieudonne, Foundations of modern analysis, Academic Press, New York (1967).
H. O. Fatorini, Relaxation in semilinear infinite dimensional control systems, Differential equations, Dynamical systems and control science, Marcel Dekker, New York (1993), 505-522.
A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486, DOI 10.1007/978-1-4612-5561-1
G. F. Webb, Continuous nonlinear perturbations of linear accretive operators in Banach spaces, J. Functional Analysis 10 (1972), 191–203. MR 0361965, DOI 10.1016/0022-1236(72)90048-1