On the Existence of Configurations of Subspaces in a Hilbert Space with Fixed Angles

Details On the Existence of Configurations of Subspaces in a Hilbert Space with Fixed Angles On the Existence of Configurations of Subspaces in a Hilbert Space with Fixed Angles

2006-05-29

arxiv.org/abs/math/0605717v1

SIGMA 2 (2006), 055, 5 pages

Mathematics

Representation Theory

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2006.055

For a class of $*$-algebras, where $*$-algebra $A_{\Gamma,\tau}$ is generated by projections associated with vertices of graph $\Gamma$ and depends on a parameter $\tau$ $(0 < \tau \leq 1)$, we study the sets $\Sigma_\Gamma$ of values of $\tau$ such that the algebras $A_{\Gamma,\tau}$ have nontrivial $*$-representations, by using the theory of spectra of graphs. In other words, we study such values of $\tau$ that the corresponding configurations of subspaces in a Hilbert space exist.

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