Commutative Banach Algebras
Commutative Banach Algebras
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交换巴纳赫代数
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
S. Goldberg
中科院分区：
文献类型：
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作者：
I. Gohberg;M. A. Kaashoek;S. Goldberg
本章包含交换巴拿赫代数的Gelfand理论。介绍并分析了Gelfand谱和Gelfand变换。通过实例对结果进行了说明。特别地，详细地解释了在Gelfand变换下，分段连续函数是如何变成连续的。特别注意有限生成的交换巴拿赫代数和由紧算子生成的巴拿赫代数。最后两节介绍了在矩阵函数分解和Wiener-Hopf积分算子中的应用。分析从乘法线性泛函的研究开始。
This chapter contains the Gelfand theory of commutative Banach algebras. The Gelfand spectrum and the Gelfand transform are introduced and analysed. The results are illustrated by various examples. In particular, it is explained in detail how under the Gelfand transformation piecewise continuous functions become continuous. Special attention is paid to finitely generated commutative Banach algebras and to the Banach algebra generated by a compact operator. The last two sections present applications to factorization of matrix functions and to Wiener-Hopf integral operators. The analysis starts with a study of multiplicative linear functionals.