Range inclusion for convex processes on Banach spaces; applications in controllability
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- by Ovidiu Cârjă
- Proc. Amer. Math. Soc. 105 (1989), 185-191
- DOI: https://doi.org/10.1090/S0002-9939-1989-0973844-0
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Abstract:
We extend the results of Mary Embry [9] on majorisation and range inclusion of bounded linear operators on Banach spaces to the case when one of the two operators is a convex process. An application in controllability is given.References
- Richard Bouldin, A counterexample in the factorization of Banach space operators, Proc. Amer. Math. Soc. 68 (1978), no. 3, 327. MR 500202, DOI 10.1090/S0002-9939-1978-0500202-8
- J. M. Borwein, Adjoint process duality, Math. Oper. Res. 8 (1983), no. 3, 403–434. MR 716121, DOI 10.1287/moor.8.3.403
- J. M. Borwein, Stability and regular points of inequality systems, J. Optim. Theory Appl. 48 (1986), no. 1, 9–52. MR 825383, DOI 10.1007/BF00938588
- Alessandra Andreini and Carla Marchiò, Continuity of minimal-time functions, Boll. Un. Mat. Ital. C (6) 3 (1984), no. 1, 109–116 (Italian, with English summary). MR 749284
- Ovidiu Cârjă, A note on admissible null controllability and on variational perturbations of the minimum time problem, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Secţ. I a Mat. 32 (1986), no. 1, 13–19. MR 893021
- O. Cârjă, On constraint controllability of linear systems in Banach spaces, J. Optim. Theory Appl. 56 (1988), no. 2, 215–225. MR 926184, DOI 10.1007/BF00939408
- Ruth F. Curtain and Anthony J. Pritchard, Infinite dimensional linear systems theory, Lecture Notes in Control and Information Sciences, vol. 8, Springer-Verlag, Berlin-New York, 1978. MR 516812
- Szymon Dolecki and David L. Russell, A general theory of observation and control, SIAM J. Control Optim. 15 (1977), no. 2, 185–220. MR 451141, DOI 10.1137/0315015
- Mary R. Embry, Factorization of operators on Banach space, Proc. Amer. Math. Soc. 38 (1973), 587–590. MR 312287, DOI 10.1090/S0002-9939-1973-0312287-8
- C. K. Fong, Range inclusion for normal derivations, Glasgow Math. J. 25 (1984), no. 2, 255–262. MR 752820, DOI 10.1017/S001708950000567X
- Sandy Grabiner, Operator ranges and invariant subspaces, Indiana Univ. Math. J. 28 (1979), no. 5, 845–857. MR 542341, DOI 10.1512/iumj.1979.28.28059
- B. E. Johnson and J. P. Williams, The range of a normal derivation, Pacific J. Math. 58 (1975), no. 1, 105–122. MR 380490
- E. A. Lifšic, Ideally convex sets, Funkcional. Anal. i Priložen. 4 (1970), no. 4, 76–77 (Russian). MR 0279568
- 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. Peichl and W. Schappacher, Constrained controllability in Banach spaces, SIAM J. Control Optim. 24 (1986), no. 6, 1261–1275. MR 861098, DOI 10.1137/0324076
- Vlastimil Pták, Some metric aspects of the open mapping and closed graph theorems, Math. Ann. 163 (1966), 95–104. MR 192316, DOI 10.1007/BF02052841
- Stephen M. Robinson, Normed convex processes, Trans. Amer. Math. Soc. 174 (1972), 127–140. MR 313769, DOI 10.1090/S0002-9947-1972-0313769-9
- R. Tyrrell Rockafellar, Monotone processes of convex and concave type, Memoirs of the American Mathematical Society, No. 77, American Mathematical Society, Providence, R.I., 1967. MR 0225231 —, Conjugate duality and optimization, SIAM, Philadelphia, Pa., 1974.
- Constantin Zălinescu, Letter to the editor: on J. M. Borwein’s paper: “Adjoint process duality” [Math. Oper. Res. 8 (1983), no. 3, 403–434; MR0716121 (85h:90092)], Math. Oper. Res. 11 (1986), no. 4, 692–698. MR 865564, DOI 10.1287/moor.11.4.692
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 185-191
- MSC: Primary 47A05; Secondary 46N05, 49E15, 93B05
- DOI: https://doi.org/10.1090/S0002-9939-1989-0973844-0
- MathSciNet review: 973844