<i>K</i> -Theory for Algebras of Operators on Banach Spaces
<i>K</i> -Theory for Algebras of Operators on Banach Spaces
It is proved that, for each pair (m, n) of non-negative integers, there is a Banach space X for which K0(B(X))≅Zm and K1(B(X))≅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 …