Infinite Norm Decompositions of C*-algebras

Arzikulov, F. N.

doi:10.1007/978-3-0348-0346-5_2

F. N. Arzikulov⁷

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 220))

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Abstract

In the given article the notion of infinite norm decomposition of a C^* -algebra is investigated. The infinite norm decomposition is some generalization of Peirce decomposition. It is proved that the infinite norm decomposition of any C^*-algebra is a C^*algebra.C^*-factors with an infinite and a nonzero finite projection and simple purely infinite C^*-algebras are constructed.

Mathematics Subject Classification (2000). Primary 46L35, 17C65; Secondary 47L30.

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References

O. Bratteli. Inductive limits of finite dimensional C ^∗ -algebras. Trans. Amer. Math. Soc. 171, pp. 195–234, (1972).
Google Scholar
F.N. Arzikulov. Infinite order and norm decompositions of C ^∗ -algebras. Int. Journal of Math. Analysis, vol. 2, no. 5–8, pp. 255–262, (2008) (www.m-hikari.com).
M. Rørdam. A simple C ^∗ -algebra with a finite and an infinite projection. Acta Math. 191, pp. 109–142 (2003).
Google Scholar
N.C. Philips. A Classification Theorem for Nuclear Purely Infinite Simple C ^∗ - Algebras. Documenta Math. No. 5, pp. 49–114, (2000).
Google Scholar
M. Rørdam. Classification of Nuclear C ^∗ -algebras. Springer, Encyclopaedia of Mathematical Sciences, Vol. 126, (2001).
Google Scholar

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Authors and Affiliations

Institute of Mathematics and Information Technologies of the National Academy of Sciences of Uzbekistan, 700143, Tashkent, Usbekistan
F. N. Arzikulov

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F. N. Arzikulov
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Correspondence to F. N. Arzikulov .

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Editors and Affiliations

Department of Mathematics, Virginia Polytechnic Institute, McBryde Hall 524, Blacksburg, 24061, Virginia, USA
Joseph A. Ball
Dept. Mathematics, University of Iowa, MacLean Hall 14, Iowa City, 52242-1419, Iowa, USA
Raúl E. Curto
, CINVESTAV, IPN - Instituto Politécnico Nacional, Av. IPN 2508, Mexico, D.F., 07360, Distrito Federal, Mexico
Sergei M. Grudsky
Dept. Mathematics, University of California, San Diego, Gilman Dr. 9500, La Jolla, 92093-0112, California, USA
J. William Helton
, Departamento di Matemática, Centro de Investigación en Matemáticas, Guanajuato, Gto., 36000, Guanajuato, Mexico
Raúl Quiroga-Barranco
Departamento de Matemática, CINVESTAV-IPN, Apdo. Postal, México, 07300, Distrito Federal, Mexico
Nikolai L. Vasilevski

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Arzikulov, F.N. (2012). Infinite Norm Decompositions of C^*-algebras. In: Ball, J., Curto, R., Grudsky, S., Helton, J., Quiroga-Barranco, R., Vasilevski, N. (eds) Recent Progress in Operator Theory and Its Applications. Operator Theory: Advances and Applications(), vol 220. Springer, Basel. https://doi.org/10.1007/978-3-0348-0346-5_2

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DOI: https://doi.org/10.1007/978-3-0348-0346-5_2
Published: 13 February 2012
Publisher Name: Springer, Basel
Print ISBN: 978-3-0348-0345-8
Online ISBN: 978-3-0348-0346-5
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