$n$-Subspaces in linear and unitary spaces

Details $n$-Subspaces in linear and unitary spaces $n$-Subspaces in linear and unitary spaces

2008-07-14

arxiv.org/abs/0807.2206v1

Mathematics

Functional Analysis

11 pages

Scientific paper

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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