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单词 NormAndSpectralRadiusInCalgebras
释义

norm and spectral radius in C*-algebras


Let 𝒜 be a C*-algebra (http://planetmath.org/CAlgebra). Let Rσ(a) denote the spectral radius of the element a𝒜.

Theorem - For every a𝒜 we have that a=Rσ(a*a).

This result shows that the norm in a C*-algebra has a purely nature. Moreover, the norm in a C*-algebra is unique (in the sense that there is no other norm for which the algebra is a C*-algebra).

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更新时间:2025/5/4 1:15:24