Tensor product of Fock spaces is analogous to the Hardy space over the unit polydisc. This plays an important role in the development of noncommutative operator theory and function theory in the sense of noncommutative polydomains and noncommutative varieties. In this paper we study joint invariant subspaces of tensor product of full Fock spaces and noncommutative varieties. We also obtain, in particular, by using techniques of noncommutative varieties, a classification of joint invariant subspaces of n-fold tensor products of Drury–Arveson spaces.

中文翻译：

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多域和非交换品种中的子模块

Fock空间的张量积类似于单位多圆盘上的Hardy空间。从非交换多域和非交换变种的意义上讲，这在非交换算子理论和函数理论的发展中起着重要作用。在本文中，我们研究了全Fock空间和非交换变数的张量积的联合不变子空间。特别是，我们还通过使用非交换变种技术，获得了Drury-Arveson空间的n倍张量积的联合不变子空间的分类。