More elementary operators that are spectrally bounded

Abstract

We discuss some necessary and some sufficient conditions for an elementary operator $x\mapsto {\sum }_{i=1}^n{a}_{i}x{b}_i$ on a Banach algebra $A$ to be spectrally bounded. In the case of length three, we obtain a complete characterisation when $A$ acts irreducibly on a Banach space of dimension greater than three.

23 pages