Spectral radius formulae in quotient 𝐶*-algebras

Abstract

If I I is a closed two-sided ideal in C ∗ {C^ * } -algebra A A , we prove spectral radius formulae for the coset x + I ( x ∈ A ) x + I(x \in A) in the quotient algebra A / I A/I . Then, as a corollary we get the main result of Mau-Hsiang Shin (Proc. Amer. Math. Soc. 100 (1987), 137-139).

On the perturbation functions and similarity orbits

“…If F · (·) = · e , the result we obtain is the same as in [11], when the C * -algebra is B(H) and I = K(H).…”