Academic Journal
The equality case in ‖f(A)‖ ≤ f(‖A‖) for analytic matrix functions under strongly stable norms.
| Title: | The equality case in ‖f(A)‖ ≤ f(‖A‖) for analytic matrix functions under strongly stable norms. |
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| Authors: | Zhang, Teng1 (AUTHOR) teng.zhang@stu.xjtu.edu.cn |
| Source: | Linear Algebra & its Applications. Dec2026, Vol. 750, p154-162. 9p. |
| Subject Terms: | *Matrix functions, *Matrix norms, *Matrix inequalities, *Operator functions, *Mathematical equivalence, *Spectral theory |
| Abstract: | 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] |
| Database: | Academic Search Index |
| ISSN: | 00243795 |
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| DOI: | 10.1016/j.laa.2026.07.011 |