Functions of perturbed pairs of noncommutative dissipative operators
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A. B. Aleksandrov and V. V. Peller;
Translated by: the authors - St. Petersburg Math. J. 34 (2023), 379-392
- DOI: https://doi.org/10.1090/spmj/1758
- Published electronically: June 7, 2023
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Abstract:
Let a function $f$ belong to the inhomogeneous analytic Besov space $(Б_{\infty ,1}^{\,1})_+(\mathbb {R}^2)$. For a pair $(L,M)$ of not necessarily commuting maximal dissipative operators, the function $f(L,M)$ of $L$ and $M$ is defined as a densely defined linear operator. For $p\in [1,2]$, it is proved that if $(L_1,M_1)$ and $(L_2,M_2)$ are pairs of not necessarily commuting maximal dissipative operators such that both differences $L_1-L_2$ and $M_1-M_2$ belong to the Schatten–von Neumann class ${\boldsymbol S}_p$, then for an arbitrary function $f$ in $(Б_{\infty ,1}^{\,1})_+(\mathbb {R}^2)$, the operator difference $f(L_1,M_1)-f(L_2,M_2)$ belongs to ${\boldsymbol S}_p$ and the following Lipschitz type estimate holds: \begin{equation*} \|f(L_1,M_1)-f(L_2,M_2)\|_{{\boldsymbol S}_p} \le const\|f\|_{Б_{\infty ,1}^{\,1}}\max \big \{\|L_1-L_2\|_{{\boldsymbol S}_p},\|M_1-M_2\|_{{\boldsymbol S}_p}\big \}. \end{equation*}References
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Bibliographic Information
- A. B. Aleksandrov
- Affiliation: St. Petersburg Department of V. A. Steklov Mathematical Institute of the Russian Academy of Sciences, 27 Fontanka, 191023 St. Petersburg, Russia
- MR Author ID: 195855
- Email: alex@pdmi.ras.ru
- V. V. Peller
- Affiliation: Department of Mathematics and Computer Science, St. Petersburg State University; and Department of Mathematics, Michigan State University, East Lansing, Michigan 48824; and St. Petersburg Department of V. A. Steklov Mathematical Institute of the Russian Academy of Sciences, 27 Fontanka, 191023 St. Petersburg, Russia
- MR Author ID: 194673
- ORCID: 0000-0002-7414-7625
- Email: peller@math.msu.edu
- Received by editor(s): October 21, 2021
- Published electronically: June 7, 2023
- Additional Notes: The research on §4–§6 is supported by Russian Science Foundation, grant no. 18-11-00053. The work is supported by a grant of the Government of the Russian Federation for the state support of scientific research, carried out under the supervision of leading scientists, agreement 075-15-2021-602
- © Copyright 2023 American Mathematical Society
- Journal: St. Petersburg Math. J. 34 (2023), 379-392
- MSC (2020): Primary 47B44; Secondary 47B10, 47A56
- DOI: https://doi.org/10.1090/spmj/1758
Dedicated: To Nikolai Kapitonovich Nikolski on the occasion of his 80th birthday