COMMUTATORS AND SQUARE-ZERO ELEMENTS IN BANACH ALGEBRAS
COMMUTATORS AND SQUARE-ZERO ELEMENTS IN BANACH ALGEBRAS
Our initial result states that, in a certain class of Banach algebras which includes |$C^*$|-algebras and group algebras of locally compact groups, every commutator lies in the closed linear span of square-zero elements. The proof relies on the theory of Banach algebras with property |${\mathbb {B}}$|. We then study several …