2008 | OriginalPaper | Buchkapitel
Extensions of σ-C* -algebras
verfasst von : Rachid El Harti
Erschienen in: Operator Algebras, Operator Theory and Applications
Verlag: Birkhäuser Basel
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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.