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Functions of normal operators under perturbations · Around

2010

Functions of normal operators under perturbations

Aleksandrov, Alexei, Peller, Vladimir, Potapov, Denis et al.

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In \cite{Pe1}, \cite{Pe2}, \cite{AP1}, \cite{AP2}, and \cite{AP3} sharp estimates for $f(A)-f(B)$ were obtained for self-adjoint operators $A$ and $B$ and for various classes of functions $f$ on the real line $\R$.

In this paper we extend those results to the case of functions of normal operators.
We show that if a function $f$ belongs to the H\"older class $\L_\a(\R^2)$, $0<\a<1$, of functions of two variables, and $N_1$ and $N_2$ are normal operators, then $\|f(N_1)-f(N_2)\|\le\const\|f\|_{\L_\a}\|N_1-N_2\|^\a$.
We obtain a more general result for functions in the space $\L_\o(\R^2)=\big\{f:~|f(\z_1)-f(\z_2)|\le\const\o(|\z_1-\z_2|)\big\}$ for an arbitrary modulus of continuity $\o$.

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Yu.L. Daletskii
1956
Earlier work this paper cites.
M.S. Birman
1967
Earlier work this paper cites.
M.S. Birman
1968
Earlier work this paper cites.
Yu.B. Farforovskaya
1968
Earlier work this paper cites.
I.C. Gohberg and M.G. Krein, Introduction to the theory of linear nonselfadjoint operators in Hilbert space,
1969
Earlier work this paper cites.
A. McIntosh
1971
Earlier work this paper cites.
Yu.B. Farforovskaya
1972
Earlier work this paper cites.
M.S. Birman
1973
Earlier work this paper cites.
B.E. Johnson
1975
Earlier work this paper cites.
J. Peetre
1976
Earlier work this paper cites.

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