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Morneau-Guérin, Frédéric (2025). Logarithmic norms [review of the book from Söderlind, Gustaf]. Mathematical Reviews.
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| Item Type: | Book Reviews |
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| Refereed: | Yes |
| Status: | Published |
| Abstract: | Gustaf Söderlind’s Logarithmic Norms is a rare kind of mathematical monograph: it takes a concept that is both underappreciated and highly versatile and elevates it to the status of a central methodological tool in applied mathematics. The book is both a rigorous theoretical treatment and a cross-disciplinary exploration of logarithmic norms as they appear in matrix theory, operator theory, nonlinear analysis, and differential equations. It succeeds in clarifying and systematizing scattered results (some quite recent), bringing coherence and depth to an often overlooked yet conceptually rich topic. Söderlind opens his book with an interesting analogy: not mentioning the logarithmic norm in operator theory is akin to writing a textbook on complex analysis without ever referring to the real part of a complex number. This introduces a core theme of the book, namely that the logarithmic norm plays a role with respect to the operator norm similar to that of the real part to the absolute value. Despite this, the logarithmic norm remains largely neglected in standard curricula and literature. Söderlind sets out to change this by offering an integrated and comprehensive treatment of the subject. |
| Additional Information: | © Copyright American Mathematical Society 2025 |
| Depositor: | Morneau-Guérin, Frédéric |
| Owner / Manager: | Frédéric Morneau-Guérin |
| Deposited: | 25 Aug 2025 15:19 |
| Last Modified: | 25 Aug 2025 15:19 |
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