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 compact manifold X with boundary ∂X. Assuming that all connected components of X have nonempty boundary, we show that K₁(𝔄) ≃ K₁(C(X)) ⊕ ker χ, where χ: K₀(C₀(T*Ẋ)) → ℤ is the topological index, T*Ẋ denoting the cotangent bundle of the interior. Also K₀(𝔄) is topologically determined. In case ∂X has torsion free K-theory, we get K₀(𝔄) ≃ K₀(C(X)) ⊕ K₁(C₀(T*Ẋ)).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc61-0-10,
author = {Severino T. Melo and Ryszard Nest and Elmar Schrohe},
title = {K-theory of Boutet de Monvel's algebra},
journal = {Banach Center Publications},
volume = {60},
year = {2003},
pages = {149-156},
zbl = {1065.19005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc61-0-10}
}
Severino T. Melo; Ryszard Nest; Elmar Schrohe. K-theory of Boutet de Monvel's algebra. Banach Center Publications, Tome 60 (2003) pp. 149-156. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc61-0-10/