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$K$-theory of $\mathrm{SG}$-pseudo-differential algebras

Author: Fabio Nicola
Journal: Proc. Amer. Math. Soc. 131 (2003), 2841-2848
MSC (2000): Primary 46L80; Secondary 58J40, 19K56
Published electronically: January 8, 2003
MathSciNet review: 1974341
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Abstract: We are concerned with the so-called ${\rm SG}$-pseudo-differential calculus. We describe the spectrum of the unital and commutative $C^\ast$-algebra given by the norm closure of the space of $0$-order pseudo-differential operators modulo compact operators; other related algebras are also considered. Finally, their $K$-theory is computed.

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Additional Information

Fabio Nicola
Affiliation: Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy

Keywords: $K$-theory, $C^\ast$-algebras, pseudo-differential operators
Received by editor(s): January 23, 2002
Received by editor(s) in revised form: April 7, 2002
Published electronically: January 8, 2003
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2003 American Mathematical Society