The Shilov boundary ideal for a separable Fréchet local operator system is the intersection of the kernels of all its Γ-boundary representations.
Dosi,MultinormedW ∗-algebras and unbounded operators, Proceedings of the American Mathematical Society,140(12), 4187-4202
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On the Shilov boundary ideal for Fr\'{e}chet local operator systems
The Shilov boundary ideal for a separable Fréchet local operator system is the intersection of the kernels of all its Γ-boundary representations.