- 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.Accepted author manuscript, 412 KB, PDF document

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

In: Journal of Mathematical Analysis and Applications, Vol. 428, No. 1, 01.08.2015, p. 282-294.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Kania, T, Koszmider, P & Laustsen, N 2015, 'Banach spaces whose algebra of bounded operators has the integers as their K0-group', *Journal of Mathematical Analysis and Applications*, vol. 428, no. 1, pp. 282-294. https://doi.org/10.1016/j.jmaa.2015.03.021

Kania, T., Koszmider, P., & Laustsen, N. (2015). Banach spaces whose algebra of bounded operators has the integers as their K0-group. *Journal of Mathematical Analysis and Applications*, *428*(1), 282-294. https://doi.org/10.1016/j.jmaa.2015.03.021

Kania T, Koszmider P, Laustsen N. Banach spaces whose algebra of bounded operators has the integers as their K0-group. Journal of Mathematical Analysis and Applications. 2015 Aug 1;428(1):282-294. Epub 2015 Mar 12. doi: 10.1016/j.jmaa.2015.03.021

@article{2f09b42649174cbdadfd3a66aad0ff2d,

title = "Banach spaces whose algebra of bounded operators has the integers as their K0-group",

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.",

keywords = "K0-group, Banach algebra, Bounded, linear operator, Banach space, Continuous functions on the first uncountable ordinal interval",

author = "Tomasz Kania and Piotr Koszmider and Niels Laustsen",

note = "The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 428 (1), 2015, {\textcopyright} ELSEVIER.",

year = "2015",

month = aug,

day = "1",

doi = "10.1016/j.jmaa.2015.03.021",

language = "English",

volume = "428",

pages = "282--294",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Banach spaces whose algebra of bounded operators has the integers as their K0-group

AU - Kania, Tomasz

AU - Koszmider, Piotr

AU - Laustsen, Niels

N1 - The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 428 (1), 2015, © ELSEVIER.

PY - 2015/8/1

Y1 - 2015/8/1

N2 - 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.

AB - 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.

KW - K0-group

KW - Banach algebra

KW - Bounded

KW - linear operator

KW - Banach space

KW - Continuous functions on the first uncountable ordinal interval

U2 - 10.1016/j.jmaa.2015.03.021

DO - 10.1016/j.jmaa.2015.03.021

M3 - Journal article

VL - 428

SP - 282

EP - 294

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -