Supporting sequences of pure states on JB algebras

Jan Hamhalter

Studia Mathematica (1999)

  • Volume: 136, Issue: 1, page 37-47
  • ISSN: 0039-3223

Abstract

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We show that any sequence ( φ n ) of mutually orthogonal pure states on a JB algebra A such that ( φ n ) forms an almost discrete sequence in the relative topology induced by the primitive ideal space of A admits a sequence ( a n ) consisting of positive, norm one, elements of A with pairwise orthogonal supports which is supporting for ( φ n ) in the sense of φ n ( a n ) = 1 for all n. Moreover, if A is separable then ( a n ) can be taken such that ( φ n ) is uniquely determined by the biorthogonality condition φ n ( a n ) = 1 . Consequences of this result improving hitherto known extension theorems for C*-algebras and descriptions of dual JB algebras are given.

How to cite

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Hamhalter, Jan. "Supporting sequences of pure states on JB algebras." Studia Mathematica 136.1 (1999): 37-47. <http://eudml.org/doc/216659>.

@article{Hamhalter1999,
abstract = {We show that any sequence $(φ_n)$ of mutually orthogonal pure states on a JB algebra A such that $(φ_n)$ forms an almost discrete sequence in the relative topology induced by the primitive ideal space of A admits a sequence $(a_n)$ consisting of positive, norm one, elements of A with pairwise orthogonal supports which is supporting for $(φ_n)$ in the sense of $φ_n(a_n)=1$ for all n. Moreover, if A is separable then $(a_n)$ can be taken such that $(φ_n)$ is uniquely determined by the biorthogonality condition $φ_n(a_n)=1$. Consequences of this result improving hitherto known extension theorems for C*-algebras and descriptions of dual JB algebras are given.},
author = {Hamhalter, Jan},
journal = {Studia Mathematica},
keywords = {pairwise orthogonal sequence; pure states; almost separated sequence; mutually orthogonal pure states of a JB-algebra; supporting orthogonal sequence; dual JB-algebra},
language = {eng},
number = {1},
pages = {37-47},
title = {Supporting sequences of pure states on JB algebras},
url = {http://eudml.org/doc/216659},
volume = {136},
year = {1999},
}

TY - JOUR
AU - Hamhalter, Jan
TI - Supporting sequences of pure states on JB algebras
JO - Studia Mathematica
PY - 1999
VL - 136
IS - 1
SP - 37
EP - 47
AB - We show that any sequence $(φ_n)$ of mutually orthogonal pure states on a JB algebra A such that $(φ_n)$ forms an almost discrete sequence in the relative topology induced by the primitive ideal space of A admits a sequence $(a_n)$ consisting of positive, norm one, elements of A with pairwise orthogonal supports which is supporting for $(φ_n)$ in the sense of $φ_n(a_n)=1$ for all n. Moreover, if A is separable then $(a_n)$ can be taken such that $(φ_n)$ is uniquely determined by the biorthogonality condition $φ_n(a_n)=1$. Consequences of this result improving hitherto known extension theorems for C*-algebras and descriptions of dual JB algebras are given.
LA - eng
KW - pairwise orthogonal sequence; pure states; almost separated sequence; mutually orthogonal pure states of a JB-algebra; supporting orthogonal sequence; dual JB-algebra
UR - http://eudml.org/doc/216659
ER -

References

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