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# On $n$-tuples of subspaces in linear and unitary spaces

### Abstract

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.

### Article Information

 Title On $n$-tuples of subspaces in linear and unitary spaces Source Methods Funct. Anal. Topology, Vol. 15 (2009), no. 1, 48-60 MathSciNet MR2502638 Copyright The Author(s) 2009 (CC BY-SA)

### Authors Information

Yu. S. Samoilenko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

D. Yu. Yakymenko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

Yu. S. Samoilenko and D. Yu. Yakymenko, On $n$-tuples of subspaces in linear and unitary spaces, Methods Funct. Anal. Topology 15 (2009), no. 1, 48-60.

### BibTex

@article {MFAT483,
AUTHOR = {Samoilenko, Yu. S. and Yakymenko, D. Yu.},
TITLE = {On $n$-tuples of subspaces in linear and unitary spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {15},
YEAR = {2009},
NUMBER = {1},
PAGES = {48-60},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=483},
}