On the standard K-loop structure of positive invertible elements in a C\*-algebra.

We investigate the algebraic properties of the operation ab=aba on the set of all positive invertible elements of a C\*-algebra A. We show that its commutativity, associativity and distributivity are each equivalent to the commutativity of A. We present abstract characterizations of the operation and a few related ones, too. [ABSTRACT FROM AUTHOR]