Relatively spectral homomorphisms and K-injectivity

Details Relatively spectral homomorphisms and K-injectivity Relatively spectral homomorphisms and K-injectivity

2010-05-13

arxiv.org/abs/1005.2430v1

Mathematics

Operator Algebras

6 pages

Scientific paper

Let $\A$ and $\B$ be unital Banach algebras and $\phi\colon\A\to\B$ be a
unital continuous homomorphism. We prove that if $\phi$ is relatively spectral
(i.e., there is a dense subalgebra $X$ of $\A$ such that
$\sp_\B(\phi(a))=\sp_\A(a)$ for every $a\in X$) and has dense range, then
$\phi$ induces monomorphisms from $K_i(\A)$ to $K_i(\B)$, $i=0,1$.

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