Banach代數中元素的譜
2022-11-12 15:18 作者:
臥煙鈴 |
我要投稿
今天這一章呢其實就是把上一題坑給填了


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證明:




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%5E%7B-1%7D%5CVert%5Cleq%5Cfrac%7B1%7D%7B1-%5CVert%20x%5CVert%7D.)
證明:

%5Ek%5Cto0)

y_n%3Dy_n(x-%20e)%3De-x%5E%7Bn%2B1%7D)
%5En%5Cto0)
y%3Dy(x-e)%3De)
%2C%E4%B8%94(e-x)%5E%7B-1%7D%3D%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20x%5En.)
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)
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證明:
)
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證明:
%5Cgeq%5Clim_%7Bn%5Cto%20%5Cinfty%7D%5CVert%20x%5En%5CVert%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D%E5%8D%B3%E5%8F%AF)
)
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%5E%7B-1%7D)%3D%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20%5Cfrac%7Bf(x%5En)%7D%7B%5Clambda%5E%7Bn%2B1%7D%7D%2C)

%7C%7D%7B(a%2B%5Cvarepsilon)%5E%7Bn%2B1%7D%7D%3C%2B%5Cinfty)
%5E%7Bn%2B1%7D%7D%5CBig)%5CBig%7C%3C%2B%5Cinfty)
由共鳴定理得
%5E%7Bn%2B1%7D%7D%5CBig%5CVert%3C%2B%5Cinfty)
%5En)

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%3D%5Cmax_%7B%5Clambda%5Cin%5Csigma(x)%7D%5Cvert%20%5Clambda%5Cvert%3D%5Clim_%7Bn%5Cto%20%5Cinfty%7D%5CVert%20x%5En%5CVert%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D.)

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