K-theory for algebras of operators on Banach spaces
Abstract
It is proved that, for each pair (m,n) of non-negative integers, there is a Banach space X for which the group K0(B(X)) is isomorphic to m copies of the integers and the group K1(B(X)) is isomorphic to n copies of the integers. Along the way we compute the K-groups of all closed ideals of operators contained in the ideal of strictly singular operators, and we derive some results about the existence of splittings of certain short exact sequences.
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