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This article is cited in 1 scientific paper (total in 1 paper)
Research Papers
Functons of perturbed pairs of noncommuting dissipative operator
A. B. Aleksandrova, V. V. Pellerbcad a С.-Петербургское отделение Математического института им. В. А. Стеклова Российской академии наук Фонтанка, 27, 191023 Санкт-Петербург, Россия
b Факультет математики и Компьютерных наук, С.-Петербургский Государственный Университет, Университетская наб., 7/9, 199034 Санкт-Петербург, Россия
c Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, USA
d Российский Университет дружбы народов (РУДН), ул. Миклухо-Маклая 6, 117198, Москва, Россия
Abstract:
Let $f$ be a function belonging to the nonhomogeneous analytic Besov space
$(\mathrm{\text{Б}}_{\infty,1}^1)_+(\mathbb{R}^2)$.
For a pair $(L,M)$ of not necessarily commuting maximal dissipative
operators, the function $f(L,M)$ is introduced as a densely defined
linear.
For $p\in[1,2]$, we prove that if $(L_1,M_1)$ and $(L_2,M_2)$ are pairs of
not necessarily commuting maximal dissipative operators such that the two
difeerences $L_1-L_2$ и $M_1-M_2$
belong to the Schatten–von Neumann class $\mathbf{S}_p$, then for every $f$ in
$(\mathrm{\text{Б}}_{\infty,1}^1)_+(\mathbb{R}^2)$ the operator difference $f(L_1,M_1)-f(L_2,M_2)$ belongs to
$\mathbf{S}_p$ and the following Lipschitz-type estimate holds true:
$
\|f(L_1,M_1)-f(L_2,M_2)\|_{\mathbf{S}_p}
\le\mathrm{const}\,\|f\|_{\mathrm{\text{Б}}_{\infty,1}^1}\max\big\{\|L_1-L_2\|_{\mathbf{S}_p},\|M_1-M_2\|_{\mathbf{S}_p}\big\}.
$
Keywords:
dissipative operator, Haagerup tensor product, Haagerup-type tensor products, semispectral measure, Besov classes, functions of noncommuting operators, Lipschitz-type estimates for functions of operators, Schatten–von Neumann classes.
Received: 21.10.2021
Citation:
A. B. Aleksandrov, V. V. Peller, “Functons of perturbed pairs of noncommuting dissipative operator”, Algebra i Analiz, 34:3 (2022), 93–114; St. Petersburg Math. J., 34:3 (2023), 379–392
Linking options:
https://www.mathnet.ru/eng/aa1810 https://www.mathnet.ru/eng/aa/v34/i3/p93
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