• Korean Journal of Mathematics
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• 제13권1호
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• pp.43-50
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• 2005

We introduce the Joint spectrum on the complex Banach space and on the complex Hilbert space and the tensor product spectrums on the tensor product spaces. And we will show ${\sigma}[P(T_1,T_2,{\ldots},T_n)]={\sigma}(T_1{\otimes}T_2{\otimes}{\cdots}{\otimes}T_n)$ on $X_1{\overline{\otimes}}X_2{\overline{\otimes}}{\cdots}{\overline{\otimes}}X_n$ for a polynomial P.

• Korean Journal of Mathematics
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• 제14권1호
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• pp.1-5
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• 2006

We will introduce tensor product spectrums on the tensor product spaces. And we will show that ${\sigma}[P(T_1,T_2,{\ldots},T_n)]=P[({\sigma}(T_1),{\sigma}(T_2){\ldots},{\sigma}(T_n)]={\sigma}(T_1,T_2{\ldots},T_n)$.

• 대한수학회보
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• 제34권4호
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• pp.525-533
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• 1997

We analysis spectral subspaces of $C^*$-algebras for a compacr group action. And we prove the condition that the fixed point algebra of the product action is the tensor product of the fixed point algebras.