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Список литературы
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|
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| 1. |
Dixmier J., “Position relative de deux variétés linéares fermées dans un espace de Hilbert”, Rev. Sci. Paris, 86 (1948), 387–399 |
| 2. |
Broise M., “Commutateurs dans le groupe unitaire d'un facteur”, J. Math. Pures Appl., 46:3 (1967), 299–312 |
| 3. |
Fillmore P. A., Topping D. M., “Operator algebras generated by projections”, Duke Math. J., 34:2 (1967), 333–336 |
| 4. |
Fillmore P. A., “Sums of operators with square zero”, Acta. Sci. Math. (Szeged), 28:3–4 (1967), 285–288 |
| 5. |
Pearcy C., Topping D. M., “Sums of small numbers of idempotents”, Michigan Math. J., 14:4 (1967), 453–465 |
| 6. |
Matsumoto K., “Self-adjoint operators as a real span of 5 projections”, Math. Japon., 29:2 (1984), 291–294 |
| 7. |
Holland S. S., Jr., “Projections algebraically generate the bounded operators on real or quaternionic Hilbert space”, Proc. Amer. Math. Soc., 123:11 (1995), 3361–3362 |
| 8. |
Бикчентаев А. М., “О представлении линейных операторов в гильбертовом пространстве в виде конечных сумм произведений проекторов”, Докл. РАН, 393:4 (2003), 444–447 |
| 9. |
Takesaki M., Theory of operator algebras, I, Springer-Verl., New York; Heidelberg; Berlin, 1979 |
| 10. |
Dixmier J., Les algèbres d'opérateurs dans l'espace Hilbertien, 2nd ed., Gauthier-Villars, Paris, 1969 |
| 11. |
Sakai S., $C^*$-algebras and $W^*$-algebras, Springer-Verl., New York; Heidelberg; Berlin, 1971 |
| 12. |
Deckard D., Pearcy C., “On matrices over ring of continuous complex valued functions on a Stonian space”, Proc. Amer. Math. Soc., 14:2 (1963), 322–328 |
| 13. |
Wegge-Olsen N. E., K-theory and $C^*$-algebras. A friendly approach, Oxford Sci. Publ., The Clarendon Press, Oxford Univ. Press, New York, 1993 |
| 14. |
Goldstein S., Paszkiewicz A., “Linear combinations of projections in von Neumann algebras”, Proc. Amer. Math. Soc., 116:1 (1992), 175–183 |
| 15. |
Marcoux L. W., Murphy G. J., “Unitarily-invariant linear spaces in $C^*$-algebras”, Proc. Amer. Math. Soc., 126:12 (1998), 3597–3605 |
| 16. |
Marcoux L. W., “On the linear span of the projections in certain simple $C^*$-algebras”, Indiana Univ. Math. J., 51:3 (2002), 753–771 |
| 17. |
Бикчентаев А. М., Шерстнев А. Н., “Проекторно-выпуклые комбинации в $C^*$-алгебрах со свойством унитарной факторизации”, Мат. заметки, 76:4 (2004), 625–628 |
| 18. |
Koliha J. J., “Range projections of idempotents in $C^*$-algebras”, Demonstratio Math., 24:1 (2001), 91–103 |
| 19. |
Kadison R. V., “Diagonalizing matrices”, Amer. J. Math., 106:6 (1984), 1451–1468 |
| 20. |
Fujii J. I., Furuta T., “Holub's factorization and normal approximations of idempotent operators”, Math. Japon., 25:1 (1980), 143–145 |
| 21. |
Fillmore P. A., “On sums of projections”, J. Funct. Anal., 4:1 (1969), 146–152 |
| 22. |
Hance-Olsen H., Størmer E., Jordan operator algebras, Pitman Publ. Inc., Boston; London; Melbourne, 1984 |
| 23. |
Бурбаки Н., Теория множеств, Мир, М., 1965 |
| 24. |
Мерфи Дж., $C^*$-алгебры и теория операторов, Факториал, М., 1997 |