Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
We consider examples of operator Lipschitz functions f for which the operator Lipschitz seminorm ‖f‖OL(ℝ) coincides with the Lipschitz seminorm ‖f‖Lip(ℝ). In particular, we consider the operator Lipschitz functions f such that |f ' (0)| = ‖f‖OL(ℝ). It is well known that f has this property if its derivative f′ is positive definite. It is proved in this paper that there are other functions having this property. It is also shown that the identity |f ' (t0)| = ‖f‖OL(ℝ) implies the continuity of f at t0. In fact, a more general statement is established concerning commutator Lipschitz functions on a closed subset of the complex plane.
Язык оригинала | английский |
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Страницы (с-по) | 176-189 |
Число страниц | 14 |
Журнал | Journal of Mathematical Sciences (United States) |
Том | 251 |
Номер выпуска | 2 |
DOI | |
Состояние | Опубликовано - 1 ноя 2020 |
Опубликовано для внешнего пользования | Да |
ID: 87314630