Spectral radius algebras and 𝐶₀ contractions

Petrovic, Srdjan

doi:10.1090/S0002-9939-08-09656-1

Spectral radius algebras and $C_0$ contractions
HTML articles powered by AMS MathViewer

by Srdjan Petrovic PDF

Proc. Amer. Math. Soc. 136 (2008), 4283-4288 Request permission

Abstract:

We consider the spectral radius algebras associated to $C_0$ contractions. If $A$ is such an operator we show that the spectral radius algebra $\mathcal {B}_A$ always properly contains the commutant of $A$.

References

Hari Bercovici, Operator theory and arithmetic in $H^\infty$, Mathematical Surveys and Monographs, vol. 26, American Mathematical Society, Providence, RI, 1988. MR 954383, DOI 10.1090/surv/026
Animikh Biswas, Alan Lambert, and Srdjan Petrovic, On spectral radius algebras and normal operators, Indiana Univ. Math. J. 56 (2007), no. 4, 1661–1674. MR 2354695, DOI 10.1512/iumj.2007.56.2907
A. Biswas, A. Lambert, S. Petrovic, and B. Weinstock, On spectral radius algebras, Operators and Matrices 2 (2008), no. 2, 167–176.
Animikh Biswas and Srdjan Petrovic, On extended eigenvalues of operators, Integral Equations Operator Theory 55 (2006), no. 2, 233–248. MR 2234256, DOI 10.1007/s00020-005-1381-5
Alan Lambert and Srdjan Petrovic, Beyond hyperinvariance for compact operators, J. Funct. Anal. 219 (2005), no. 1, 93–108. MR 2108360, DOI 10.1016/j.jfa.2004.06.001
Srdjan Petrovic, On the extended eigenvalues of some Volterra operators, Integral Equations Operator Theory 57 (2007), no. 4, 593–598. MR 2313287, DOI 10.1007/s00020-006-1477-6