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Factoring weakly compact operators
and the inhomogeneous Cauchy problem

Author: Diómedes Bárcenas
Journal: Proc. Amer. Math. Soc. 128 (2000), 1357-1360
MSC (1991): Primary 34C10; Secondary 47H20
Published electronically: October 18, 1999
MathSciNet review: 1641633
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] D. Bárcenas and W. Urbina, Measurable Multifunctions in non separable Banach spaces, SIAM, J. Math. Anal. 28, (1997), 1212-1226. CMP 97:17
  • [2] W. J. Davis, T. Figiel, W. B. Johnson, and A. Pełczyński, Factoring weakly compact operators, J. Functional Analysis 17 (1974), 311–327. MR 0355536
  • [3] O. Diekman, S. A. van Gils, S. M. Verduyn Lunel and H. O. Wather, , Springer Verlag, Berlin, 1995.
  • [4] J. Dieudonne, , Academic Press, New York (1967).
  • [5] H. O. Fatorini, , Marcel Dekker, New York (1993), 505-522.
  • [6] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486
  • [7] G. F. Webb, Continuous nonlinear perturbations of linear accretive operators in Banach spaces, J. Functional Analysis 10 (1972), 191–203. MR 0361965

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Additional Information

Diómedes Bárcenas
Affiliation: Departamento de Mathemáticas, Universidad de los Andes, Mérida 5101, Venezuela

Keywords: Semigroup of compact operators, Lipschitz continuous functions, strong solutions
Received by editor(s): December 3, 1997
Received by editor(s) in revised form: June 22, 1998
Published electronically: October 18, 1999
Additional Notes: This research was partially supported by CDCHT of ULA under project C840-97.
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society