K-theory for algebras of operators on Banach spaces
Functional Analysis
2008-02-03 v1
Abstract
It is proved that, for each pair (m,n) of non-negative integers, there is a Banach space X for which the group K_0(B(X)) is isomorphic to m copies of the integers and the group K_1(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.
Cite
@article{arxiv.math/9701206,
title = {K-theory for algebras of operators on Banach spaces},
author = {Niels Jakob Laustsen},
journal= {arXiv preprint arXiv:math/9701206},
year = {2008}
}