K-Theory of an Algebra of Pseudodifferential Operators on a Noncompact Manifold

Patrícia Hess; Severino T. Melo

Authors

Patrícia Hess Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-090 São Paulo, Brazil.
Severino T. Melo Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-090 São Paulo, Brazil.

Keywords:

K-Theory, pseudodifferential operators

Abstract

Let ð’œ denote the C*-algebra of bounded operators on L²(â„ × ð•Š¹) generated by: all multiplications a(M) by functions a â‹² C^âˆž(ð•Š¹), all multiplications b(M) by functions b â‹² C([âˆ’âˆž,+âˆž]), all multiplications by 2Ï€-periodic continuous functions, Î› = (1 âˆ’ Î”_{â„×ð•Š¹} )^âˆ’1/2, where Î”_{â„×ð•Š¹} is the Laplacian operator on L²(â„ × ð•Š¹), and Ï‘_tÎ›, Ï‘_xÎ›, for t â‹² â„ and xâ‹² ð•Š¹. We compute the K-theory of ð’œ and of its quotient by the ideal of compact operators.