States on unital partially-ordered groups

Anatolij Dvurečenskij

Kybernetika (2002)

  • Volume: 38, Issue: 3, page [297]-318
  • ISSN: 0023-5954

Abstract

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We study states on unital po-groups which are not necessarily commutative as normalized positive real-valued group homomorphisms. We show that in contrast to the commutative case, there are examples of unital po-groups having no state. We introduce the state interpolation property holding in any Abelian unital po-group, and we show that it holds in any normal-valued unital ℓ -group. We present a connection among states and ideals of po-groups, and we describe extremal states on the state space of unital po-groups.

How to cite

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Dvurečenskij, Anatolij. "States on unital partially-ordered groups." Kybernetika 38.3 (2002): [297]-318. <http://eudml.org/doc/33584>.

@article{Dvurečenskij2002,
abstract = {We study states on unital po-groups which are not necessarily commutative as normalized positive real-valued group homomorphisms. We show that in contrast to the commutative case, there are examples of unital po-groups having no state. We introduce the state interpolation property holding in any Abelian unital po-group, and we show that it holds in any normal-valued unital $\ell $-group. We present a connection among states and ideals of po-groups, and we describe extremal states on the state space of unital po-groups.},
author = {Dvurečenskij, Anatolij},
journal = {Kybernetika},
keywords = {non-commutative group; partially ordered groups; non-commutative group; partially ordered groups},
language = {eng},
number = {3},
pages = {[297]-318},
publisher = {Institute of Information Theory and Automation AS CR},
title = {States on unital partially-ordered groups},
url = {http://eudml.org/doc/33584},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Dvurečenskij, Anatolij
TI - States on unital partially-ordered groups
JO - Kybernetika
PY - 2002
PB - Institute of Information Theory and Automation AS CR
VL - 38
IS - 3
SP - [297]
EP - 318
AB - We study states on unital po-groups which are not necessarily commutative as normalized positive real-valued group homomorphisms. We show that in contrast to the commutative case, there are examples of unital po-groups having no state. We introduce the state interpolation property holding in any Abelian unital po-group, and we show that it holds in any normal-valued unital $\ell $-group. We present a connection among states and ideals of po-groups, and we describe extremal states on the state space of unital po-groups.
LA - eng
KW - non-commutative group; partially ordered groups; non-commutative group; partially ordered groups
UR - http://eudml.org/doc/33584
ER -

References

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