On Centre Properties of Irreducible Subalgebras of Compact Elementary Operators

Abstract/Overview

In this paper, we characterize the centre of dense irreducible subalgebras of compact elementary operators that are spectrally bounded. We show that the centre is a unital, irreducible and commutative C∗ -subalgebra. Furthermore, the supports from the centre are orthogonal and the intersection of a nonzero ideal with the centre is non-zero.