对偶算子代数和对偶算子空间的森田嵌入

arXiv: Operator Algebras Pub Date : 2017-04-14 DOI:10.4064/SM170427-15-8

G. Eleftherakis

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引用次数: 2

摘要

我们定义了对偶算子代数的关系<。如果在A中存在一个投影p使得B和pAp在我们的意义上是森田等价的，我们说B < A。我们证明了<是可传递的，并研究了以下问题:如果A < B和B < A，那么A和B是稳定同构的吗?我们提出了对偶算子空间的一个类似关系<，并给出了在这种情况下<的一些性质。

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Morita embeddings for dual operator algebras and dual operator spaces

We define a relation < for dual operator algebras. We say that B < A if there exists a projection p in A such that B and pAp are Morita equivalent in our sense. We show that < is transitive, and we investigate the following question: If A < B and B < A, then is it true that A and B are stably isomorphic? We propose an analogous relation < for dual operator spaces, and we present some properties of < in this case.

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arXiv: Operator Algebras

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