Pure states on Jordan algebras

Jan Hamhalter

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 1, page 81-91
  • ISSN: 0862-7959

Abstract

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We prove that a pure state on a C * -algebras or a JB algebra is a unique extension of some pure state on a singly generated subalgebra if and only if its left kernel has a countable approximative unit. In particular, any pure state on a separable JB algebra is uniquely determined by some singly generated subalgebra. By contrast, only normal pure states on JBW algebras are determined by singly generated subalgebras, which provides a new characterization of normal pure states. As an application we contribute to the extension problem and strengthen the hitherto known results on independence of operator algebras arising in the quantum field theory.

How to cite

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Hamhalter, Jan. "Pure states on Jordan algebras." Mathematica Bohemica 126.1 (2001): 81-91. <http://eudml.org/doc/248840>.

@article{Hamhalter2001,
abstract = {We prove that a pure state on a $C^\{\ast \}$-algebras or a JB algebra is a unique extension of some pure state on a singly generated subalgebra if and only if its left kernel has a countable approximative unit. In particular, any pure state on a separable JB algebra is uniquely determined by some singly generated subalgebra. By contrast, only normal pure states on JBW algebras are determined by singly generated subalgebras, which provides a new characterization of normal pure states. As an application we contribute to the extension problem and strengthen the hitherto known results on independence of operator algebras arising in the quantum field theory.},
author = {Hamhalter, Jan},
journal = {Mathematica Bohemica},
keywords = {JB algebras; $C^\{\ast \}$-algebras; pure states; state space independence of Jordan algebras; normal pure states on JBW algebras; JB algebras; -algebras; pure states; state space independence of Jordan algebras; normal pure states on JBW algebras},
language = {eng},
number = {1},
pages = {81-91},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Pure states on Jordan algebras},
url = {http://eudml.org/doc/248840},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Hamhalter, Jan
TI - Pure states on Jordan algebras
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 1
SP - 81
EP - 91
AB - We prove that a pure state on a $C^{\ast }$-algebras or a JB algebra is a unique extension of some pure state on a singly generated subalgebra if and only if its left kernel has a countable approximative unit. In particular, any pure state on a separable JB algebra is uniquely determined by some singly generated subalgebra. By contrast, only normal pure states on JBW algebras are determined by singly generated subalgebras, which provides a new characterization of normal pure states. As an application we contribute to the extension problem and strengthen the hitherto known results on independence of operator algebras arising in the quantum field theory.
LA - eng
KW - JB algebras; $C^{\ast }$-algebras; pure states; state space independence of Jordan algebras; normal pure states on JBW algebras; JB algebras; -algebras; pure states; state space independence of Jordan algebras; normal pure states on JBW algebras
UR - http://eudml.org/doc/248840
ER -

References

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