The Calkin image of algebras of singular integral operators (Q915097)

Let \({\mathcal A}\) be a Banach algebra of singular integral operators in \(L_ p(\Gamma,W)\) with piecewise continuous coefficient on the curves \(\Gamma\) with corners and intersections, W a Khvedelidse weight. The authors give the description of the image \({\mathcal A}^{\pi}\) in the Calkin algebra of the Banach algebra \({\mathcal A}\). Another very interesting result is that the algebra \({\mathcal A}^{\pi}\) remains invariant if the curve \(\Gamma\) is replaced by another curve \(\Gamma '\) being only homeomorphic to \(\Gamma\) and if the weight W is replaced by any other Khvedelidse weight. The authors discuss some applications of the main results so as symbol calculus, norm estimation, algebras with Carleman shift and with conjugation.