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http://dx.doi.org/10.4134/JKMS.j180138

Q-MEASURES ON THE DUAL UNIT BALL OF A JB⁎-TRIPLE  

Edwards, C. Martin (The Queen's College)
Oliveira, Lina (Center for Mathematical Analysis, Geometry and Dynamical Systems)
Publication Information
Journal of the Korean Mathematical Society / v.56, no.1, 2019 , pp. 197-224 More about this Journal
Abstract
Let A be a $JB^*$-triple with Banach dual space $A^*$ and bi-dual the $JBW^*$-triple $A^{**}$. Elements x of $A^*$ of norm one may be regarded as normalised 'Q-measures' defined on the complete ortho-lattice ${\tilde{\mathcal{U}}}(A^{**})$ of tripotents in $A^{**}$. A Q-measure x possesses a support e(x) in ${\tilde{\mathcal{U}}}(A^{**})$ and a compact support $e_c(x)$ in the complete atomic lattice ${\tilde{\mathcal{U}}}_c(A)$ of elements of ${\tilde{\mathcal{U}}}(A^{**})$ compact relative to A. Necessary and sufficient conditions for an element v of ${\tilde{\mathcal{U}}}_c(A)$ to be a compact support tripotent $e_c(x)$ are given, one of which is related to the Q-covering numbers of v by families of elements of ${\tilde{\mathcal{U}}}_c(A)$.
Keywords
$JB^*$-triple; $C^*$-algebra; Q-topology; Q-measure; compact support tripotent;
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