Excision in Banach simplicial and cyclic cohomology

Details Excision in Banach simplicial and cyclic cohomology Excision in Banach simplicial and cyclic cohomology

1996-06-07

arxiv.org/abs/math/9606212v1

Mathematics

Operator Algebras

Scientific paper

We prove that, for every extension of Banach algebras $ 0 \rightarrow B \rightarrow A \rightarrow D \rightarrow 0 $ such that $B$ has a left or right bounded approximate identity, the existence of an associated long exact sequence of Banach simplicial or cyclic cohomology groups is equivalent to the existence of one for homology groups. It follows from the continuous version of a result of Wodzicki that associated long exact sequences exist. In particular, they exist for every extension of $C^*$-algebras.

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