论文标题
亚产系统和非交通函数理论的张量代数
Tensor algebras of subproduct systems and noncommutative function theory
论文作者
论文摘要
我们重新访问带有希尔伯特太空纤维的亚产品系统的张量代数，在无限尺寸纤维的情况下解决了一些开放问题。 We characterize when a tensor algebra can be identified as the algebra of uniformly continuous noncommutative functions on a noncommutative homogeneous variety or, equivalently, when it is residually finite dimensional: this happens precisely when the closed homogeneous ideal associated to the subproduct system satisfies a Nullstellensatz with respect to the algebra of uniformly continuous noncommutative functions on the非交通闭合单位球。我们表明，与有限的尺寸情况相反，在无限尺寸纤维的情况下，该零stellensatz可能会失败。最后，我们还解决了亚产物系统的张量代数的同构问题：当且仅当其亚量亚产物系统在适当的意义上是同构时，两个这样的张量代数是（同态）同构的。
We revisit tensor algebras of subproduct systems with Hilbert space fibers, resolving some open questions in the case of infinite dimensional fibers. We characterize when a tensor algebra can be identified as the algebra of uniformly continuous noncommutative functions on a noncommutative homogeneous variety or, equivalently, when it is residually finite dimensional: this happens precisely when the closed homogeneous ideal associated to the subproduct system satisfies a Nullstellensatz with respect to the algebra of uniformly continuous noncommutative functions on the noncommutative closed unit ball. We show that - in contrast to the finite dimensional case - in the case of infinite dimensional fibers this Nullstellensatz may fail. Finally, we also resolve the isomorphism problem for tensor algebras of subproduct systems: two such tensor algebras are (isometrically) isomorphic if and only if their subproduct systems are isomorphic in an appropriate sense.
