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Factoring weakly compact operators and the inhomogeneous Cauchy problem
Author(s):
Diómedes
Bárcenas
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1357-1360.
MSC (1991):
Primary 34C10;
Secondary 47H20
Posted:
October 18, 1999
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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:
- [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. Fiegel, W. B. Johnson and A. Pelczynsky, Factoring weakly compact Operators, J. Functional Analysis, 17, (1974), 311-327. MR 50:8010
- [3]
- O. Diekman, S. A. van Gils, S. M. Verduyn Lunel and H. O. Wather, , Springer Verlag, Berlin, 1995.
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- J. Dieudonne, , Academic Press, New York (1967).
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- H. O. Fatorini, , Marcel Dekker, New York (1993), 505-522.
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- [7]
- G. F. Webb, Continuous nonlinear perturbations of linear accretive operators in Banach spaces, J. Funct. Anal., 10, (1972), 191-203. MR 50:14407
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Additional Information:
Diómedes
Bárcenas
Affiliation:
Departamento de Mathemáticas, Universidad de los Andes, Mérida 5101, Venezuela
Email:
barcenas@ciens.ula.ve
DOI:
10.1090/S0002-9939-99-05127-8
PII:
S 0002-9939(99)05127-8
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
Posted:
October 18, 1999
Additional Notes:
This research was partially supported by CDCHT of ULA under project C840-97.
Communicated by:
David R. Larson
Copyright of article:
Copyright
2000,
American Mathematical Society
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