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).

Title norm and spectral radius in C*-algebras
Canonical name NormAndSpectralRadiusInCalgebras
Date of creation 2013-03-22 17:38:41
Last modified on 2013-03-22 17:38:41
Owner asteroid (17536)
Last modified by asteroid (17536)
Numerical id 7
Author asteroid (17536)
Entry type Theorem
Classification msc 46L05
Related topic HomomorphismsOfCAlgebrasAreContinuous
Related topic CAlgebra