{"ID":22938771,"CreatedAt":"2026-09-17T01:37:05.451791504Z","UpdatedAt":"2026-09-17T01:37:05.451791504Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.18619","arxiv_id":"2609.18619","title":"Linear maps preserving Kasparov cycles and the characterization of induced automorphisms","abstract":"Let $E$ be a Hilbert C*-module and $\\mathcal{L}(E)$ the C*-algebra of all bounded adjointable operators on $E$. An operator $T \\in \\mathcal{L}(E)$ is a Kasparov cycle if $T^*T - 1$ and $TT^*-1$ are compact operators on $E$. If $\\mathcal{L}(E)\\rightarrow \\mathcal{L}(E)$ is a prime C*-algebra, and $\\varphi:\\mathcal{L}(E)\\rightarrow \\mathcal{L}(E)$ is a linear map which is unital and surjective up to compact operators, and preserves Kasparov cycles in both directions, then the induced map $ψ:\\mathcal{L}(E)/\\mathcal{K}(E) \\rightarrow \\mathcal{L}(E)/\\mathcal{K}(E)$ is either a $*$-automorphism or a $*$-anti-automorphism. Our work extends the main result of [J. Math. Anal. Appl. 354 (2009), 625-629] to the set of Kasparov cycles, showing that the assumption ``$\\mathcal{L}(E)/\\mathcal{K}(E)$ has real rank zero'' is redundant in our results.","short_abstract":"Let $E$ be a Hilbert C*-module and $\\mathcal{L}(E)$ the C*-algebra of all bounded adjointable operators on $E$. An operator $T \\in \\mathcal{L}(E)$ is a Kasparov cycle if $T^*T - 1$ and $TT^*-1$ are compact operators on $E$. If $\\mathcal{L}(E)\\rightarrow \\mathcal{L}(E)$ is a prime C*-algebra, and $\\varphi:\\mathcal{L}(E)...","url_abs":"https://arxiv.org/abs/2609.18619","url_pdf":"https://arxiv.org/pdf/2609.18619v1","authors":"[\"Kamran Sharifi\"]","published":"2026-09-16T13:09:47Z","proceeding":"math.OA","tasks":"[\"math.OA\"]","methods":"[]","has_code":false}