$K$-theory of $\mathrm {SG}$-pseudo-differential algebras
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Abstract:
We are concerned with the so-called $\textrm {SG}$-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.References
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Additional Information
- Fabio Nicola
- Affiliation: Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy
- Email: nicola@dm.unito.it
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2841-2848
- MSC (2000): Primary 46L80; Secondary 58J40, 19K56
- DOI: https://doi.org/10.1090/S0002-9939-03-06837-0
- MathSciNet review: 1974341