Geodesic
Simultaneous reduction to block triangular form and theorems on pairs of complex idempotents
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 979-982 
Kh. D. Ikramov. Simultaneous reduction to block triangular form and theorems on pairs of complex idempotents. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 979-982. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a1/
@article{ZVMMF_2011_51_6_a1,
     author = {Kh. D. Ikramov},
     title = {Simultaneous reduction to block triangular form and theorems on pairs of complex idempotents},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {979--982},
     year = {2011},
     volume = {51},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a1/}
}
TY  - JOUR
AU  - Kh. D. Ikramov
TI  - Simultaneous reduction to block triangular form and theorems on pairs of complex idempotents
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 979
EP  - 982
VL  - 51
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a1/
LA  - ru
ID  - ZVMMF_2011_51_6_a1
ER  - 
%0 Journal Article
%A Kh. D. Ikramov
%T Simultaneous reduction to block triangular form and theorems on pairs of complex idempotents
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 979-982
%V 51
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a1/
%G ru
%F ZVMMF_2011_51_6_a1

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

It is shown that the properties of idempotents found in recent journal publications can be justified in an easier way if a classical theorem concerning the simultaneous reduction of a pair of complex idempotents to block triangular form is used.

[1] Blichfeldt H. F., Finite collineation groups, Univ. Chicago Press, Chicago, 1917

[2] Ikramov Kh. D., “Ob odnovremennoi privodimosti k blochno-treugolnomu vidu par kosykh proektorov”, Zh. vychisl. matem. i matem. fiz., 38:2 (1998), 181–182 | MR | Zbl

[3] Roch S., Silbermann B., “Algebras generated by idempotents and the symbol calculus for singular integral operaz tors”, Integral Equat. Operator Theory, 11 (1988), 385–419 | DOI | MR | Zbl

[4] Gohberg I., Krupnik N., “Extension theorems for invertibility symbols in Banach algebras”, Integral Equat. Operator Theory, 15 (1992), 991–1010 | DOI | Zbl

[5] Gohberg I., Krupnik N., “Extension theorems for Fredholm and invertibility symbols”, Integral Equat. Operator Theory, 16 (1993), 514–529 | DOI | Zbl

[6] Böttcher A., Spitkovsky I. M., “A gentle guide to the basics of two projections theory”, Linear Algebra Appl., 432 (2010), 1412–1459 | DOI | MR

[7] Gross J., Trenkler G., “Nonsingularity of the difference of two oblique projectors”, SIAM J. Matrix Anal. Appl., 21:2 (1999), 390–395 | DOI | MR | Zbl

[8] Zuo K., “Nonsingularity of the difference and the sum of two idempotent matrices”, Linear Algebra Appl., 433 (2010), 476–482 | DOI | MR | Zbl