Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2018.02.28
  • Accepted : 2018.08.02
  • Published : 2019.01.01
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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 ${\tilde{\mathcal{U}}}_c(A)$.

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References

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