Title: On spectral radius algebras and normal operators

Authors: Animikh Biswas, Alan Lambert and Srdjan Petrovic

Issue: Volume 56 (2007), Issue 4, 1661-1674

Abstract: We associate to each normal operator $N$ an algebra $\mathcal{B}_N$ that contains the commutant of $N$. For a subclass of normal operators we demonstrate that $\mathcal{B}_N$ has a nontrivial invariant subspace. Further, we show that $\mathcal{B}_N$ properly contains the commutant of $N$ so that the invariant subspace result is stronger then the existence of a hyperinvariant subspace.