Geodesic
On the spectrum of $C^*$-algebras generated by pseudodifferential operators with discontinuous symbols
Izvestiya. Mathematics , Tome 23 (1984) no. 3, pp. 525-544.

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This article deals with a $C^*$-algebra $\mathscr A'$ generated by pseudodifferential operators whose symbols can have discontinuities “of the first kind” at a finite number of points. The set of points of discontinuity depends on the operator, and after completion of the algebra $\mathscr A/\mathscr K$, where $\mathscr K$ the ideal of compact operators, there appear classes (elements of the quotient algebra) whose symbols have dense sets of singularities. A complete set of irreducible representations is determined for the quotient algebra $\mathscr A/\mathscr K$, and the Jacobson topology on the spectrum is described. The same problems are solved also for the algebra $\mathscr A$. It is established that $\mathscr A$ and $\mathscr A/\mathscr K$ are algebras of type I. Bibliography: 7 titles. 
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B. A. Plamenevskii; V. N. Senichkin. On the spectrum of $C^*$-algebras generated by pseudodifferential operators with discontinuous symbols. Izvestiya. Mathematics , Tome 23 (1984) no. 3, pp. 525-544. http://geodesic.mathdoc.fr/item/IM2_1984_23_3_a6/

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