The Calkin image of algebras of singular integral operators
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.
Banach algebra of singular integral operators
scientific article; zbMATH DE number 4151161
scientific article