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

Full Text

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},
}