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Zapiski Nauchnykh Seminarov POMI, 2019, Volume 480, Pages 26–47 (Mi znsl6763)  

This article is cited in 1 scientific paper (total in 1 paper)

Some remarks concerning operator Lipschitz functions

A. B. Aleksandrov

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Full-text PDF (265 kB) Citations (1)
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Abstract: We consider examples of operator Lipschitz functions $f$ for which the operator Lipschitz seminorm $\|f\|_{\mathrm{OL}(\mathbb{R})}$ coincides with the Lipschitz seminorm $\|f\|_{\mathrm{Lip}(\mathbb{R})}$. In particular, we consider the operator Lipschitz functions such that $f'(0)=\|f\|_{\mathrm{OL}(\mathbb{R})}$. It is well known that every function $f$ whose the derivative $f'$ is positive definite has this property. In the paper it is proved that there are other functions having this property. It is also shown that the identity $|f'(t_0)|=\|f\|_{\mathrm{OL}(\mathbb{R})}$ implies that the derivative of $f$ is continuous at $t_0$. In fact, a more general statement is established concerning commutator Lipschitz functions on a closed subset of the complex plane.
Key words and phrases: operator Lipschitz functions.
Funding agency Grant number
Russian Science Foundation 18-11-00053
Received: 26.08.2019
Document Type: Article
UDC: 517.98
Language: Russian
Citation: A. B. Aleksandrov, “Some remarks concerning operator Lipschitz functions”, Investigations on linear operators and function theory. Part 47, Zap. Nauchn. Sem. POMI, 480, ПОМИ, СПб., 2019, 26–47
Citation in format AMSBIB
\Bibitem{Ale19}
\by A.~B.~Aleksandrov
\paper Some remarks concerning operator Lipschitz functions
\inbook Investigations on linear operators and function theory. Part~47
\serial Zap. Nauchn. Sem. POMI
\yr 2019
\vol 480
\pages 26--47
\publ ПОМИ
\publaddr СПб.
\mathnet{http://mi.mathnet.ru/znsl6763}
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  • https://www.mathnet.ru/eng/znsl/v480/p26
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Записки научных семинаров ПОМИ
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