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MULTIPLICATIVE SPECTRAL FUNCTIONALS ON
Bulletin of the Australian Mathematical Society ( IF 0.6 ) Pub Date : 2020-01-08 , DOI: 10.1017/s0004972719001242 C. TOURÉ , R. BRITS
Bulletin of the Australian Mathematical Society ( IF 0.6 ) Pub Date : 2020-01-08 , DOI: 10.1017/s0004972719001242 C. TOURÉ , R. BRITS
If $A$ is a commutative $C^{\star }$ -algebra and if $\unicode[STIX]{x1D719}:A\rightarrow \mathbb{C}$ is a continuous multiplicative functional such that $\unicode[STIX]{x1D719}(x)$ belongs to the spectrum of $x$ for each $x\in A$ , then $\unicode[STIX]{x1D719}$ is linear and hence a character of $A$ . This establishes a multiplicative Gleason–Kahane–Żelazko theorem for $C(X)$ .
中文翻译:
多重谱函数
如果$澳元 是可交换的$C^{\星}$ -代数和如果$\unicode[STIX]{x1D719}:A\rightarrow \mathbb{C}$ 是一个连续的乘法泛函,使得$\unicode[STIX]{x1D719}(x)$ 属于谱系$x$ 对于每个$x\in 澳元 , 然后$\unicode[STIX]{x1D719}$ 是线性的,因此具有$澳元 . 这建立了一个乘法 Gleason-Kahane-Żelazko 定理$C(X)$ .
更新日期:2020-01-08
中文翻译:
多重谱函数
如果