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},
}