C*-Structure and K-Theory of Boutet de Monvel's Algebra
| dc.creator | Melo, S. T. | |
| dc.creator | Nest, R. | |
| dc.creator | Schrohe, E. | |
| dc.date | 2001-10-23 | |
| dc.date | 2002-10-03 | |
| dc.date.accessioned | 2026-07-07T04:44:01Z | |
| dc.date.available | 2026-07-07T04:44:01Z | |
| dc.description | We consider the norm closure $A$ of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a manifold $X$ with boundary $Y$. We first describe the image and the kernel of the continuous extension of the boundary principal symbol to $A$. If the $X$ is connected and $Y$ is not empty, we then show that the K-groups of $A$ are topologically determined. In case the manifold, its boundary and the tangent space of the interior have torsion-free K-theory, we prove that $K_i(A/K)$ is isomorphic to the direct sum of $K_i(C(X))$ and $K_{1-i}(C_0(TX'))$, for i=0,1, with $K$ denoting the compact ideal and $TX'$ the tangent bundle of the interior of $X$. Using Boutet de Monvel's index theorem, we also prove this result for i=1 without assuming the torsion-free hypothesis. We also give a composition sequence for $A$. | |
| dc.description | Final version, to appear in J. Reine Angew. Math. Improved K-theoretic results | |
| dc.identifier | https://arxiv.org/abs/math/0110253 | |
| dc.identifier | http://arxiv.org/abs/math/0110253 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62471 | |
| dc.subject | Operator Algebras | |
| dc.subject | Analysis of PDEs | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 58J40; 46L80; 58J32; 35S15; 19K56 | |
| dc.title | C*-Structure and K-Theory of Boutet de Monvel's Algebra | |
| dc.type | text |