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Journal of the London Mathematical Society 1999 59(2):715-728; doi:10.1112/S0024610799007206
© 1999 by London Mathematical Society
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© The London Mathematical Society

K-Theory for Algebras of Operators on Banach Spaces

Niels Jakob Laustsen

Department of Mathematics and Computer Science, Odense University Campusvej 55, DK-5230 Odense M, Denmark laustsen{at}imada.ou.dk

Received 20 January 1997. Revision received 18 June 1997.

It is proved that, for each pair (m, n) of non-negative integers, there is a Banach space X for which K0(B(X)){cong}Zm and K1(B(X)){cong}Zn. The K-groups of all closed ideals of operators contained in the ideal of strictly singular operators are computed, and some results about the existence of splittings of certain short exact sequences are derived.

Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT laustsen{at}amsta.leeds.ac.uk


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