Banach algebras with involution
Banach algebras with involution
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具有对合的 Banach 代数
DOI：
10.1007/bf01304613
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发表时间：
1972
影响因子：
0.6
通讯作者：
V. Pták
中科院分区：
文献类型：
--
作者：
V. Pták
在这一讲中，我们打算报告有关对合的巴拿赫代数理论的一些最新结果。它们都是基于大约一年前发现的厄米代数中的一个不等式，这个不等式给厄米代数理论和C*代数的抽象表征带来了相当大的改进。让我们首先回顾一些定义和已知的结果。给定一个希尔伯特空间，如果我们用B (H)表示H上所有有界线性算子的集合，如果我们赋予它算子范数和通常的代数结构，它就成为一个Banach代数。此外，它还带有自然的对合，即分配给每个对象的映射
In this lecture we intend to present a report about some recent results in the theory of Banach algebras with involution. They are all based on an inequality in hermitian algebras discovered about a year ago which has brought considerable improvements in the theory of hermitian algebras as well as in abstract characterizations of C*-algebras.Let us begin by recalling some definitions and known results. Given a Hilbert space if, we denote by B (H) the set of all bounded linear operators on H. It becomes a Banach algebra if we equip it with the operator norm and the usual algebraic structure. Also, it carries a natural involution, the mapping which assigns to each