Representations of a compact group on a Banach space
Representations of a compact group on a Banach space
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Banach 空间上紧群的表示
DOI：
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发表时间：
1955
期刊：
影响因子：
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通讯作者：
K. Shiga
中科院分区：
文献类型：
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作者：
K. Shiga
设$G$是紧群，$mathfrak{N}$是复赋范线性空间。我们通过表示${mathfrak{N}，T(A)}$表示$G$到$mathfrak{N}$上的有界线性算子群的同态，使得$a
右行T(A)$。下列类型的表示是重要的：i)代数表示，ii)有界代数表示，i)弱可测表示，2)iv)强可测表示，3)v)弱连续表示，4)vi)强连续表示。当的表示空间$mathfrak{N}$
Let $G$ be a compact group and $mathfrak{N}$ a complex normed linear space. We mean by a representation ${mathfrak{N}, T(a)}$ a homomorphism of $G$ into the group of bounded linear operators on $mathfrak{N}$ such that $a
ightarrow T(a)$ . The following types of representations are important: i) algebraic repre $cdot$ sentation, ii) bounded algebraic representation,i) iii) weakly measurable representation,2) iv) strongly measurable representation,3) v) weakly continuous representation,4) vi) strongly continuous representation.5) Clearly each condition above becomes gradually stronger when it runs from i) to vi), except iv). When the representation space $mathfrak{N}$ of