Stable Isomorphisms of Operator Algebras
Stable Isomorphisms of Operator Algebras
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算子代数的稳定同构
DOI：
10.1093/imrn/rnad146
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发表时间：
2023
影响因子：
1
通讯作者：
Kakariadis E
中科院分区：
文献类型：
--
作者：
Kakariadis E
具有-同构对角线的算子代数和表示紧算子。证明了若和等距同构，则和等距同构。如果代数和满足一个额外的解析性条件，则用任何包含紧算子的算子代数来代替时，类似的结果也成立.对于nonselfadjoint图代数这意味着该图是一个完整的不变量的各种类型的同构，包括稳定的同构，从而加强了最近的结果Dor-On，Eilers和格芬。类似的结果证明了代数的对角线满足取消和有-群同构。这对研究各种半交叉积之间的稳定同构有意义。
Letandbe operator algebras with-isomorphic diagonals and letdenote the compact operators. We show that ifandare isometrically isomorphic, thenandare isometrically isomorphic. If the algebrasandsatisfy an extra analyticity condition a similar result holds withbeing replaced by any operator algebra containing the compact operators. For nonselfadjoint graph algebras this implies that the graph is a complete invariant for various types of isomorphisms, including stable isomorphisms, thus strengthening a recent result of Dor-On, Eilers, and Geffen. Similar results are proven for algebras whose diagonals satisfy cancellation and have-groups isomorphic to. This has implications in the study of stable isomorphisms between various semicrossed products.