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Extensions of σ-C* -algebras

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Operator Algebras, Operator Theory and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 181))

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Abstract

Let A be a σ-C*-algebra. The bounded part b(A) of A introduced by Konrad Schmüdgen in [4] is a C*-algebra for some C*-norm. We shall show that if A is a split extension of a σ-C*-algebra B by a closed two-sided ideal I then b(A) will be a split extension of the C*-algebra b(B) by the closed two-sided b(I). A number of results concerning the bounded part of a σ-C*-algebra are established.

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References

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Author information

Authors and Affiliations

  1. University Hassan I., FST de Settat., Bp 577, Settat, Morocco

    Rachid El Harti

Authors
  1. Rachid El Harti
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Editor information

Editors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, U.T.L., Avenida Rovisco Pais, 1049-001, Lisboa, Portugal

    Maria Amélia Bastos , Amarino Brites Lebre  & Frank-Olme Speck ,  & 

  2. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    Israel Gohberg

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© 2008 Birkhäuser Verlag Basel/Switzerland

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El Harti, R. (2008). Extensions of σ-C* -algebras. In: Bastos, M.A., Lebre, A.B., Speck, FO., Gohberg, I. (eds) Operator Algebras, Operator Theory and Applications. Operator Theory: Advances and Applications, vol 181. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8684-9_9

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