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# On the graph $K_{1,n}$ related configurations of subspaces of a Hilbert space

### Abstract

We study systems of subspaces $H_1,\dots,H_N$ of a complex Hilbert space H that satisfy the following conditions: for every index $k > 1$, the set $\{\theta_{k,1},\ldots,\theta_{k,m_k}\}$ of angles $\theta_{k,i}\in(0,\pi/2)$ between $H_1$ and $H_k$ is fixed; all other pairs $H_k$, $H_j$ are orthogonal. The main tool in the study is a construction of a system of subspaces of a Hilbert space on the basis of its Gram operator (the G-construction).

Key words: System of subspaces, Hilbert space, orthogonal projections, Gram operator.

### Article Information

 Title On the graph $K_{1,n}$ related configurations of subspaces of a Hilbert space Source Methods Funct. Anal. Topology, Vol. 23 (2017), no. 3, 285-300 MathSciNet MR3707523 Milestones Received 23/03/2017 Copyright The Author(s) 2017 (CC BY-SA)

### Authors Information

Alexander Strelets
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine

### Citation Example

Alexander Strelets, On the graph $K_{1,n}$ related configurations of subspaces of a Hilbert space, Methods Funct. Anal. Topology 23 (2017), no. 3, 285-300.

### BibTex

@article {MFAT990,
AUTHOR = {Strelets, Alexander},
TITLE = {On the graph $K_{1,n}$ related configurations of subspaces of a Hilbert space},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {23},
YEAR = {2017},
NUMBER = {3},
PAGES = {285-300},
ISSN = {1029-3531},
MRNUMBER = {MR3707523},
URL = {http://mfat.imath.kiev.ua/article/?id=990},
}

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