Complete Normed Algebras
Complete Normed Algebras
复制标题
DOI：
10.1007/978-3-642-65669-9
复制
发表时间：
1973-06
期刊：
影响因子：
--
通讯作者：
F. Bonsall;J. Duncan
中科院分区：
文献类型：
--
作者：
F. Bonsall;J. Duncan
一个复杂的Banach代数的公理是非常愉快的选择。它们足够简单，允许广泛的应用领域，特别是在调和分析，算子理论和函数代数。在同一时间，他们是足够紧，以允许发展的丰富收集的结果，主要是通过相互作用的基本部分的理论解析函数，环，和Banach空间。许多定理是非常美丽的东西，简单的声明，令人惊讶的内容，和优雅的证明。我们相信，其中一些值得每一个数学家知道。这本书的目的是给一个帐户的主要方法和结果在理论的Banach代数，交换和非交换。必须适用某些排除原则，以便使我们的任务不超出范围。某些具体的Banach代数类有非常丰富的文献，即C*-代数，函数代数和群代数。我们认为这些高度发展的理论不属于我们的研究范围。我们并没有完全回避它们，而是关注它们在一般理论中的地位，而没有进一步发展它们的特殊性质。由于空间和时间的原因，我们已经省略了某些其他议题，这将很自然地已列入，特别是理论的乘数和扩展的Banach代数，以及影响Banach代数的一些标准代数条件环。
The axioms of a complex Banach algebra were very happily chosen. They are simple enough to allow wide ranging fields of application, notably in harmonic analysis, operator theory and function algebras. At the same time they are tight enough to allow the development of a rich collection of results, mainly through the interplay of the elementary parts of the theories of analytic functions, rings, and Banach spaces. Many of the theorems are things of great beauty, simple in statement, surprising in content, and elegant in proof. We believe that some of them deserve to be known by every mathematician. The aim of this book is to give an account of the principal methods and results in the theory of Banach algebras, both commutative and non commutative. It has been necessary to apply certain exclusion principles in order to keep our task within bounds. Certain classes of concrete Banach algebras have a very rich literature, namely C*-algebras, function algebras, and group algebras. We have regarded these highly developed theories as falling outside our scope. We have not entirely avoided them, but have been concerned with their place in the general theory, and have stopped short of developing their special properties. For reasons of space and time we have omitted certain other topics which would quite naturally have been included, in particular the theories of multipliers and of extensions of Banach algebras, and the implications for Banach algebras of some of the standard algebraic conditions on rings.