Symmetrization of the symbol in Banach algebras generated by idempotents (Q1264497)

It is known that a Banach algebra \(A\) generated by \(2N\) idempotents satisfying certain relations is an algebra with matrix symbol of order \(2N\), which is completely and explicitly defined via the spectra of two elements. In the case when \(A\) is a \(C^*\)-algebra, this symbol is not symmetric. The paper describes some additional conditions on the algebra \(A\) in order to define explicitly a symmetric symbol.