Relatively spectral homomorphisms and K-injectivity

DOI10.7153/OAM-05-09zbMATH Open1216.46046arXiv1005.2430OpenAlexW2962820516WikidataQ122643316 ScholiaQ122643316MaRDI QIDQ5390292

Yifeng Xue

Publication date: 1 April 2011

Published in: Operators and Matrices (Search for Journal in Brave)

Abstract: Let $A$ and $B$ be unital Banach algebras and $phicolonAoB$ 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 $s{p}_B(phi(a))=s{p}_A(a)$ for every $ainX$) and has dense range, then $phi$ induces monomorphisms from $K_i(A)$ to $K_i(B)$, $i=0,1$.

Full work available at URL: https://arxiv.org/abs/1005.2430

zbMATH Keywords

K-theoryunital Banach algebradense rangerelatively spectral homomorphism

Mathematics Subject Classification ID

(K)-theory and operator algebras (19K99) Topological algebras, normed rings and algebras, Banach algebras (46H99)

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