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- 저자 : Lina Oliveira (검색결과 2 건)
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Q-MEASURES ON THE DUAL UNIT BALL OF A JB<sup>⁎</sup>-TRIPLE
Edwards, C. Martin,Oliveira, Lina Korean Mathematical Society 2019 대한수학회지 Vol.56 No.1
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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Q-measures on the dual unit ball of a JB${}^*$-triple
C. Martin Edwards,Lina Oliveira 대한수학회 2019 대한수학회지 Vol.56 No.1
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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