Extensions of σ-C* -algebras
Let A be a σ-C*-algebra. The bounded part b(A) of A introduced by Konrad Schmüdgen in  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.
KeywordsC*-algebra split extension multipliers algebra spectrum
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- N.C. Phillips, Inverse limits of C*-algebras, in Operator algebras and applications, Vol. I, London Math. Soc., Lecture Note Ser. 135, pages 127–185, Cambridge University Press, Cambridge (1988).Google Scholar