On n-Tuples of Subspaces in Linear and Unitary Spaces
We study a relation between brick n-tuples of subspaces of a finite dimensional linear space, and irreducible n-tuples of subspaces of a finite dimensional Hilbert (unitary) space such that a linear combination, with positive coefficients, of orthogonal projections onto these subspaces equals the id...
Збережено в:
| Дата: | 2009 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/5700 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On n-Tuples of Subspaces in Linear and Unitary Spaces / Yu.S. Samoilenko, D.Yu. Yakymenko // Methods of Functional Analysis and Topology. — 2009. — Т. 15, № 1. — С. 48–60. — Библиогр.: 34 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We study a relation between brick n-tuples of subspaces of a finite dimensional linear space, and irreducible n-tuples of subspaces of a finite dimensional Hilbert (unitary) space such that a linear combination, with positive coefficients, of orthogonal projections onto these subspaces equals the identity operator. We prove that brick systems of one-dimensional subspaces and the systems obtained from them by applying the Coxeter functors (in particular, all brick triples and quadruples of subspaces) can be unitarized. For each brick triple and quadruple of subspaces, we describe sets of characters that admit a unitarization. |
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