Range inclusion for convex processes on Banach spaces; applications in controllability

Cârjă, Ovidiu

doi:10.1090/S0002-9939-1989-0973844-0

Range inclusion for convex processes on Banach spaces; applications in controllability
HTML articles powered by AMS MathViewer

by Ovidiu Cârjă PDF

Proc. Amer. Math. Soc. 105 (1989), 185-191 Request permission

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

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