norm and spectral radius in $C^{*}$ -algebras

Let $\\mathcal{A}$ be a $C^{*}$ -algebra (http://planetmath.org/CAlgebra). Let $R_{\\sigma}(a)$ denote the spectral radius of the element $a\\in\\mathcal{A}$ .

Theorem - For every $a\\in\\mathcal{A}$ we have that $\\|a\\|=\\sqrt{R_{\\sigma}(a^{*}a)}$ .

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).

单词	NormAndSpectralRadiusInCalgebras
释义	norm and spectral radius in $C^{}$ -algebras Let $\\mathcal{A}$ be a $C^{}$ -algebra (http://planetmath.org/CAlgebra). Let $R_{\\sigma}(a)$ denote the spectral radius of the element $a\\in\\mathcal{A}$ . Theorem - For every $a\\in\\mathcal{A}$ we have that $\\\|a\\\|=\\sqrt{R_{\\sigma}(a^{}a)}$ . 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).
随便看	Sidon set SiegelKlingenTheorem Siegel-Klingen Theorem SiegelsAxiom SiegelsTheorem SiegelsTheoremOnPrimesInArithmeticProgressions Siegel’s axiom Siegel’s theorem Siegel’s theorem on primes in arithmetic progressions SierpinskiConjecture SierpinskiErdHosEgyptianFractionConjecture Sierpinski Erdős egyptian fraction conjecture SierpinskiGasket SierpinskiNumber Sierpinski number SierpinskiSetOfEuclideanPlane SierpinskiSpace Sierpinski space Sierpiński conjecture Sierpiński gasket Sierpiński set of Euclidean plane SieveOfEratosthenes sieve of Eratosthenes sieve of Eratosthenes SieveOfEratosthenes1

norm and spectral radius in C*-algebras

norm and spectral radius in $C^{*}$ -algebras