Geodesic
Approximation of Dual Spaces and Dual Operators
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2008), pp. 31-38
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the connection between equations which approximate the initial abstract linear equation and the adjoint one. We prove that the operator which is adjoint to the approximating one approximates the adjoint operator. As examples we consider adjoint linear integral equations and mutually dual linear programming problems.
Keywords: dual space, dual operator, approximation, linear programming, Fredholm integral equations. 
@article{IVM_2008_10_a3,
     author = {N. B. Pleschinskii and {\CYRK}. Sh. Mu{\cyrl}hutdinov},
     title = {Approximation of {Dual} {Spaces} and {Dual} {Operators}},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {31--38},
     year = {2008},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_10_a3/}
}
TY  - JOUR
AU  - N. B. Pleschinskii
AU  - К. Sh. Muлhutdinov
TI  - Approximation of Dual Spaces and Dual Operators
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2008
SP  - 31
EP  - 38
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/IVM_2008_10_a3/
LA  - ru
ID  - IVM_2008_10_a3
ER  - 
%0 Journal Article
%A N. B. Pleschinskii
%A К. Sh. Muлhutdinov
%T Approximation of Dual Spaces and Dual Operators
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2008
%P 31-38
%N 10
%U http://geodesic.mathdoc.fr/item/IVM_2008_10_a3/
%G ru
%F IVM_2008_10_a3
N. B. Pleschinskii; К. Sh. Muлhutdinov. Approximation of Dual Spaces and Dual Operators. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2008), pp. 31-38. http://geodesic.mathdoc.fr/item/IVM_2008_10_a3/

[1] Mikhlin S. G., Lektsii po lineinym integralnym uravneniyam, Fizmatgiz, M., 1959, 232 pp. | MR

[2] Trenogin V. A., Funktsionalnyi analiz, Nauka, M., 1980, 496 pp. | MR | Zbl

[3] Edvards R., Funktsionalnyi analiz. Teoriya i prilozheniya, Mir, M., 1969, 1072 pp. | MR

[4] Pleschinskii N. B., “K abstraktnoi teorii priblizhennykh metodov resheniya lineinykh operatornykh uravnenii”, Izv. vuzov. Matematika, 2000, no. 3, 39–47 | MR

[5] Mukhutdinov R. Sh., “Ob approksimatsii zadach lineinogo programmirovaniya”, Matem. modelirovanie i matem. fizika, Tr. Matem. tsentra im. N. I. Lobachevskogo, 32, Izd-vo Kazansk. matem. ob-va, Kazan, 2005, 31–40

[6] Ashmanov S. A., Lineinoe programmirovanie, Nauka, M., 1981, 304 pp. | MR | Zbl

[7] Pleschinskii N. B., “Abstraktnaya teoriya priblizhennykh metodov resheniya lineinykh zadach”, Chisl. metody resheniya lineinykh i nelin. zadach, Tr. Matem. tsentra im. N. I. Lobachevskogo, 13, Izd-vo DAS, Kazan, 2001, 54–75 | MR