Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615202 | Journal of Mathematical Analysis and Applications | 2015 | 13 Pages |
Abstract
Let X and Y be Banach spaces such that the ideal of operators which factor through Y has codimension one in the Banach algebra B(X) of all bounded operators on X, and suppose that Y contains a complemented subspace which is isomorphic to YâY and that X is isomorphic to XâZ for every complemented subspace Z of Y. Then the K0-group of B(X) is isomorphic to the additive group Z of integers. A number of Banach spaces which satisfy the above conditions are identified. Notably, it follows that K0(B(C([0,Ï1])))â
Z, where C([0,Ï1]) denotes the Banach space of scalar-valued, continuous functions defined on the compact Hausdorff space of ordinals not exceeding the first uncountable ordinal Ï1, endowed with the order topology.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Tomasz Kania, Piotr Koszmider, Niels Jakob Laustsen,