Similarity problems and completely bounded maps
Similarity problems and completely bounded maps
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DOI：
10.1007/978-3-662-21537-1
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发表时间：
1995-11
期刊：
影响因子：
--
通讯作者：
G. Pisier
中科院分区：
文献类型：
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作者：
G. Pisier
这些笔记围绕着三个相似问题，出现在三种不同的背景下，但都涉及复希尔伯特空间H上所有有界算子的空间B (H)第一个涉及群表示，第二个涉及C*-代数，第三个涉及圆盘代数。我们将在接下来的介绍中详细描述它们。本卷致力于必要的背景了解这三个问题，在一些特殊情况下已知的解决方案和众多相关的概念，结果，反例或扩展，他们的调查已经产生。虽然这三个问题看起来不同，但可以使用“完全有界性”的关键概念将它们放在一个共同的框架中，我们将详细介绍这个概念。利用这个概念，这三个问题都可以表述为：对于满足某些附加代数恒等式的线性映射，“有界性”是否意味着“完全有界性”。
These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B (H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C*-algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. While the three problems seem different, it is possible to place them in a common framework using the key concept of" complete boundedness", which we present in detail. Using this notion, the three problems can all be formulated as asking whether" boundedness" implies" complete boundedness" for linear maps satisfying certain additional algebraic identities.