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  • K0groupIntegers

    Rights statement: The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 428 (1), 2015, © ELSEVIER.

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

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<mark>Journal publication date</mark>1/08/2015
<mark>Journal</mark>Journal of Mathematical Analysis and Applications
Issue number1
Volume428
Number of pages13
Pages (from-to)282-294
Publication StatusPublished
Early online date12/03/15
<mark>Original language</mark>English

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.

Bibliographic note

The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 428 (1), 2015, © ELSEVIER.