Supporting sequences of pure states on JB algebras

Hamhalter, Jan

Hamhalter, Jan

Studia Mathematica, Tome 133 (1999), p. 37-47 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 1999-01-01

Zbl 0939.46036

EUDML-ID : urn:eudml:doc:216659

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     author = {Jan Hamhalter},
     title = {Supporting sequences of pure states on JB algebras},
     journal = {Studia Mathematica},
     volume = {133},
     year = {1999},
     pages = {37-47},
     zbl = {0939.46036},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv136i1p37bwm}
}

Hamhalter, Jan. Supporting sequences of pure states on JB algebras. Studia Mathematica, Tome 133 (1999) pp. 37-47. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv136i1p37bwm/

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