Open Access

# Some remarks on Hilbert representations of posets

### Abstract

For a certain class of finite posets, we prove that all their irreducible orthoscalar representations are finite-dimensional and describe those, for which there exist essential (non-degenerate) irreducible orthoscalar representations.

Key words: Representations of posets, orthoscalar representations

### Article Information

 Title Some remarks on Hilbert representations of posets Source Methods Funct. Anal. Topology, Vol. 20 (2014), no. 2, 149–163 MathSciNet MR3242863 zbMATH 1313.47034 Milestones Received 09/12/2013 Copyright The Author(s) 2014 (CC BY-SA)

### Authors Information

V. Ostrovskyi
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine

S. Rabanovich
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine

### Citation Example

V. Ostrovskyi and S. Rabanovich, Some remarks on Hilbert representations of posets, Methods Funct. Anal. Topology 20 (2014), no. 2, 149–163.

### BibTex

@article {MFAT837,
AUTHOR = {Ostrovskyi, V. and Rabanovich, S.},
TITLE = {Some remarks on Hilbert representations of posets},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {20},
YEAR = {2014},
NUMBER = {2},
PAGES = {149–163},
ISSN = {1029-3531},
MRNUMBER = {MR3242863},
ZBLNUMBER = {1313.47034},
URL = {http://mfat.imath.kiev.ua/article/?id=837},
}