On Centre Properties of Irreducible Subalgebras of Compact Elementary Operators

Abstract

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.