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Algebra i Analiz, 2022, Volume 34, Issue 3, Pages 93–114 (Mi aa1810)  

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
References:
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
English version:
St. Petersburg Mathematical Journal, 2023, Volume 34, Issue 3, Pages 379–392
DOI: https://doi.org/10.1090/spmj/1758
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
\Bibitem{AlePel22}
\by A.~B.~Aleksandrov, V.~V.~Peller
\paper Functons of perturbed pairs of noncommuting dissipative operator
\jour Algebra i Analiz
\yr 2022
\vol 34
\issue 3
\pages 93--114
\mathnet{http://mi.mathnet.ru/aa1810}
\transl
\jour St. Petersburg Math. J.
\yr 2023
\vol 34
\issue 3
\pages 379--392
\crossref{https://doi.org/10.1090/spmj/1758}
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  • This publication is cited in the following 1 articles:
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    Алгебра и анализ St. Petersburg Mathematical Journal
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