Geodesic
Invertibility of linear $f$-order preservers
Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 3, pp. 3-11.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we prove that monotonic linear transformations with respect to partial orders $\stackrel{*}{}_f$, ${*}\kern1pt{}_f$, ${}\kern1pt{*}_f$, $\stackrel{\diamond}{}_f$, $\stackrel{\sigma}{}_f$ and $\stackrel{\sigma_1}{}_f$ are invertible. 
@article{FPM_2003_9_3_a0,
     author = {A. A. Alieva},
     title = {Invertibility of linear $f$-order preservers},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {3--11},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2003_9_3_a0/}
}
TY  - JOUR
AU  - A. A. Alieva
TI  - Invertibility of linear $f$-order preservers
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2003
SP  - 3
EP  - 11
VL  - 9
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2003_9_3_a0/
LA  - ru
ID  - FPM_2003_9_3_a0
ER  - 
%0 Journal Article
%A A. A. Alieva
%T Invertibility of linear $f$-order preservers
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2003
%P 3-11
%V 9
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2003_9_3_a0/
%G ru
%F FPM_2003_9_3_a0
A. A. Alieva. Invertibility of linear $f$-order preservers. Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 3, pp. 3-11. http://geodesic.mathdoc.fr/item/FPM_2003_9_3_a0/

[1] Alieva A., Guterman A., “Monotone linear transformations on matrices are invertible”, Comm. Algebra (to appear) | MR

[2] Baksalary J. K., Hauke J., “Partial orderings on matrices referring to singular values or eigenvalues”, Linear Algebra Appl., 96 (1987), 17–26 | DOI | MR | Zbl

[3] Baksalary J. K., Hauke J., “A further algebraic version of Cochran's theorem and matrix partial orderings”, Linear Algebra Appl., 127 (1990), 157–169 | DOI | MR | Zbl

[4] Baksalary J. K., Mitra S. K., “Left-star and right-star partial orderings”, Linear Algebra Appl., 149 (1991), 73–89 | DOI | MR | Zbl

[5] Baksalary J. K., Pukelsheim F., Styan G. P. H., “Some properties of matrix partial orderings”, Linear Algebra Appl., 119 (1989), 57–85 | DOI | MR | Zbl

[6] Drazin M. P., “Natural structures on semigroups with involution”, Bull. Amer. Math. Soc., 84:1 (1978), 139–141 | DOI | MR | Zbl

[7] Gro{\fontfamily{cmr}\selectfont ß J., “A note on rank-subtractivity ordering”, Linear Algebra Appl., 289 (1999), 151–160 | DOI | MR | Zbl

[8] Hartwig R. E., “How to partially order regular elements”, Math. Japonica, 25:1 (1980), 1–13 | MR | Zbl

[9] Hauke J., Markiewicz A., Szulc T., “Inter- and extrapolatory properties of matrix partial orderings”, Linear Algebra Appl., 332–334 (2001), 437–445 | DOI | MR | Zbl

[10] Li C.-K., Tsing N.-K., “Linear preserver problems: A brief introduction and some special techniques”, Linear Algebra Appl., 162–164 (1992), 217–235 | DOI | MR | Zbl

[11] Nambooripad K. S. S., “The natural partial order on a regular semigroup”, Proc. Edinburgh Math. Soc., 23 (1980), 249–260 | DOI | MR | Zbl

[12] Pierce S. and others, “A survey of linear preserver problems”, Linear and Multilinear Algebra, 33 (1992), 1–119 | Zbl