Extensions of ordering sets of states from effect algebras onto their MacNeille completions

Jiří Janda; Zdenka Riečanová

doi:10.29007/lkdv

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Extensions of ordering sets of states from effect algebras onto their MacNeille completions

4 pages•Published: July 28, 2014

Jiří Janda and Zdenka Riecanova

Abstract

In [Riečanová Z, Zajac M.: Hilbert Space Effect-Representations of Effect Algebras] it was shown that an effect algebra E with an ordering set M of states can by embedded into a Hilbert space effect algebra E(l<sub>2</sub>(M)). We consider the problem when its effect algebraic MacNeille completion Ê can be also embedded into the same Hilbert space effect algebra E(l<sub>2</sub>(M)). That is when the ordering set M of states on E can be be extended to an ordering set of states on Ê. We give an answer for all Archimedean MV-effect algebras and Archimedean atomic lattice effect algebras.

Keyphrases: effect algebra, Hilbert space effect-representation, MacNeille completion, MV-effect algebra, positive linear operators in Hilbert space

In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 101--104

Links:	https://easychair.org/publications/paper/kSs5
	https://doi.org/10.29007/lkdv

BibTeX entry

@inproceedings{TACL2013:Extensions_of_ordering_sets,
  author    = {Ji\textbackslash{}v\{r\}\textbackslash{}'i Janda and Zdenka Rie\textbackslash{}v\{c\}anov\textbackslash{}'a},
  title     = {Extensions of ordering sets of states from effect algebras onto their MacNeille completions},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  pages     = {101--104},
  year      = {2014},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/kSs5},
  doi       = {10.29007/lkdv}}

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