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The equality case in ‖f(A)‖ ≤ f(‖A‖) for analytic matrix functions under strongly stable norms.

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Τίτλος: The equality case in ‖f(A)‖ ≤ f(‖A‖) for analytic matrix functions under strongly stable norms.
Συγγραφείς: Zhang, Teng1 (AUTHOR) teng.zhang@stu.xjtu.edu.cn
Πηγή: Linear Algebra & its Applications. Dec2026, Vol. 750, p154-162. 9p.
Θεματικοί όροι: *Matrix functions, *Matrix norms, *Matrix inequalities, *Operator functions, *Mathematical equivalence, *Spectral theory
Περίληψη: Let ‖ ⋅ ‖ be a strongly stable norm on M n (C) , and let f (z) = ∑ k = 0 ∞ c k z k be analytic in the disc | z | < R , where R ∈ (0 , ∞ ]. Assume that c k ≥ 0 for all k ≥ 0 , that c 0 (‖ I ‖ − 1) = 0 , and that there exists N ≥ 0 such that c N , c N + 1 , ... , c N + n > 0. We prove that for every matrix A ∈ M n (C) satisfying ‖ A ‖ < R , ‖ f (A) ‖ = f (‖ A ‖) ⟺ ‖ A ‖ ∈ σ (A) , where σ (A) is the spectrum of A. Consequently, this resolves a conjecture of Bünger and Rump in [2]. [ABSTRACT FROM AUTHOR]
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  Data: The equality case in ‖f(A)‖ ≤ f(‖A‖) for analytic matrix functions under strongly stable norms.
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  Data: &lt;searchLink fieldCode=&quot;JN&quot; term=&quot;%22Linear+Algebra+%26+its+Applications%22&quot;&gt;Linear Algebra &amp; its Applications&lt;/searchLink&gt;. Dec2026, Vol. 750, p154-162. 9p.
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  Data: *&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Matrix+functions%22&quot;&gt;Matrix functions&lt;/searchLink&gt;&lt;br /&gt;*&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Matrix+norms%22&quot;&gt;Matrix norms&lt;/searchLink&gt;&lt;br /&gt;*&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Matrix+inequalities%22&quot;&gt;Matrix inequalities&lt;/searchLink&gt;&lt;br /&gt;*&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Operator+functions%22&quot;&gt;Operator functions&lt;/searchLink&gt;&lt;br /&gt;*&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Mathematical+equivalence%22&quot;&gt;Mathematical equivalence&lt;/searchLink&gt;&lt;br /&gt;*&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Spectral+theory%22&quot;&gt;Spectral theory&lt;/searchLink&gt;
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  Data: Let ‖ ⋅ ‖ be a strongly stable norm on M n (C) , and let f (z) = ∑ k = 0 ∞ c k z k be analytic in the disc | z | &lt; R , where R ∈ (0 , ∞ ]. Assume that c k ≥ 0 for all k ≥ 0 , that c 0 (‖ I ‖ − 1) = 0 , and that there exists N ≥ 0 such that c N , c N + 1 , ... , c N + n &gt; 0. We prove that for every matrix A ∈ M n (C) satisfying ‖ A ‖ &lt; R , ‖ f (A) ‖ = f (‖ A ‖) ⟺ ‖ A ‖ ∈ σ (A) , where σ (A) is the spectrum of A. Consequently, this resolves a conjecture of B&#252;nger and Rump in [2]. [ABSTRACT FROM AUTHOR]
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        Value: 10.1016/j.laa.2026.07.011
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      – Code: eng
        Text: English
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        PageCount: 9
        StartPage: 154
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      – SubjectFull: Matrix functions
        Type: general
      – SubjectFull: Matrix norms
        Type: general
      – SubjectFull: Matrix inequalities
        Type: general
      – SubjectFull: Operator functions
        Type: general
      – SubjectFull: Mathematical equivalence
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      – SubjectFull: Spectral theory
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      – TitleFull: The equality case in ‖f(A)‖ ≤ f(‖A‖) for analytic matrix functions under strongly stable norms.
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            – D: 01
              M: 12
              Text: Dec2026
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              Y: 2026
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