The main objects under study are quotients of multiplier algebras of certain complete Nevanlinna--Pick spaces, examples of which include the Drury--Arveson space on the ball and the Dirichlet space on the disc. We are particularly interested in the non-commutative Choquet boundaries for these quotients. Arveson's notion of hyperrigidity is shown to be detectable through the essential normality of some natural multiplication operators, thus extending previously known results on the Arveson--Douglas conjecture. We also highlight how the non-commutative Choquet boundaries of these quotients are intertwined with their Gelfand transforms being completely isometric. Finally, we isolate analytic and topological conditions on the so-called supports of the underlying ideals that clarify the nature of the non-commutative Choquet boundaries.

中文翻译：

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完全 Nevanlinna-Pick 商的 Gelfand 变换和边界表示

研究的主要对象是某些完全 Nevanlinna-Pick 空间的乘数代数的商，例如球上的 Drury-Arveson 空间和圆盘上的 Dirichlet 空间。我们对这些商的非交换 Choquet 边界特别感兴趣。阿维森的超刚性概念被证明可以通过一些自然乘法算子的基本正态性来检测，从而扩展了先前已知的阿维森-道格拉斯猜想的结果。我们还强调了这些商的非交换 Choquet 边界如何与其完全等距的 Gelfand 变换交织在一起。最后，我们在阐明非交换 Choquet 边界的性质的潜在理想的所谓支持上分离了分析和拓扑条件。