Abstract
One of the classes of extensions which are more general than those of the ideal of compact operators K(H), for which we have the Brown-Douglas-Fillmore theory ([2],[3]), are the extensions of CO(X)⊗K(H) where X is locally compact. A class of such extensions, the homogeneous ones, for X compact have been studied in ([8],[10]) (see [7] for a more general theory). The op-posite case appears to be that of the singular extensions, i.e. those for which the extension is “localised” in a certain sense at infinity in the Alexandrov compactification of X. Such extensions have been considered by Delaroche ([4]) and in connection with the C*-algebra of the Heisenberg group, by several authors ([9], [7], [11]). The structure of such extensions appears to be rather mysterious. This is due in part to the complicated structure of the “Calkin algebra” corresponding to a singular extension problem. This “Calkin algebra” is far from being simple and the aim of the present note is to classify its closed two-sided ideals.
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© 1981 Springer Basel AG
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Pimsner, M., Popa, S., Voiculescu, D. (1981). Remarks on Ideals of the Calkin-Algebra for Certain Singular Extensions. In: Apostol, C., Douglas, R.G., Nagy, B.S., Voiculescu, D., Arsene, G. (eds) Topics in Modern Operator Theory. Operator Theory: Advances and Applications, vol 2. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5456-6_17
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DOI: https://doi.org/10.1007/978-3-0348-5456-6_17
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