Banach spaces whose algebra of bounded operators has the integers as their K0-group

Kania, Tomasz and Koszmider, Piotr and Laustsen, Niels (2015) Banach spaces whose algebra of bounded operators has the integers as their K0-group. Journal of Mathematical Analysis and Applications, 428 (1). pp. 282-294. ISSN 0022-247X

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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 Y⊕Y and that X is isomorphic to X⊕Z 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,ω1])))≅Z, where C([0,ω1]) denotes the Banach space of scalar-valued, continuous functions defined on the compact Hausdorff space of ordinals not exceeding the first uncountable ordinal ω1, endowed with the order topology.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Mathematical Analysis and Applications
Additional Information:
The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 428 (1), 2015, © ELSEVIER.
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2604
Subjects:
ID Code:
73315
Deposited By:
Deposited On:
17 Mar 2015 10:52
Refereed?:
Yes
Published?:
Published
Last Modified:
05 Jul 2020 04:21