Asymptotic Behavior of Gelfand-naimark Decomposition
نویسنده
چکیده
LetX = LσU be the Gelfand-Naimark decomposition of X ∈ GLn(C), where L is unit lower triangular, σ is a permutation matrix, and U is upper triangular. Call u(X) := diagU the u-component of X. We show that in a Zariski dense open subset of the ω-orbit of certain Bruhat decomposition, lim m→∞ |u(X)| = diag (|λω(1)|, · · · , |λω(n)|). The other situations where lim m→∞ |u(X)| converge to different limits or diverge are also discussed.
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