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K-THEORY FOR ALGEBRAS OF OPERATORS ON BANACH SPACES

Published online by Cambridge University Press:  01 April 1999

NIELS JAKOB LAUSTSEN
NIELS JAKOB LAUSTSEN
Affiliation:
Department of Mathematics and Computer Science, Odense University, Campusvej 55, DK-5230 Odense M, Denmark; [email protected] Current address: Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT; [email protected]
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Abstract

It is proved that, for each pair (m, n) of non-negative integers, there is a Banach space [Xfr ] for which K0([Bscr ]([Xfr ]))≅ℤm and K1([Bscr ]([Xfr ]))≅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.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 715 - 728
Copyright
The London Mathematical Society 1999

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