# Supporting sequences of pure states on JB algebras

Studia Mathematica (1999)

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

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topHamhalter, 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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