论文标题
Dirichlet操作员代数的表示
Representations of Dirichlet Operator Algebras
论文作者
论文摘要
dirichlet操作员代数是一个非自动接合操作员代数$ \ nathcal {a} $，属性属性$ \ nathcal {a} + \ nathcal {a} + \ nathcal {a}^*$在c $^*$ - $ \ nathcal a} $ dixtions $ c $^*$ - a}中，$ \ y r \ act。完全订购了一个完全合同表示$ \ {π_i\} $的属性，即$π_i（\ Mathcal {a}）$不变子空间被完全订购，因此，对于所有$ a \ in \ nathcal in \ Mathcal {a} = \ sup_i ||π_i（a）||。$ DIRICHLET代数类别包括最大的三角形AF代数，某些半正式产品代数和cuntz c $^*$ algebras的仪表subsalgebras。 主要的工具是基本上主eTale groupoids的二元性理论。
A Dirichlet operator algebra is a nonself-adjoint operator algebra $\mathcal{A}$ with the property that $\mathcal{A} + \mathcal{A}^*$ is norm-dense in the C$^*$-envelope of $\mathcal{A}.$ We show that, under certain restrictions, $\mathcal{A}$ has a family of completely contractive representations $\{π_i\}$ with the property that the invariant subspaces of $π_i(\mathcal{A})$ are totally ordered, and such that, for all $a \in \mathcal{A}, \ ||a|| = \sup_i ||π_i(a)||.$ The class of Dirichlet algebras includes strongly maximal triangular AF algebras, certain semicrossed product algebras, and gauge-invariant subalgebras of Cuntz C$^*$-algebras. The main tool is the duality theory for essentially principal etale groupoids.
