6 citations · 17 across the 14 of their papers we have counts for
5 papers · 1 filter
Functions of operators under perturbations of class $\bS_p$
A. B. Aleksandrov, V. V. Peller
This is a continuation of our paper \cite{AP2}. We prove that for functions in the Hölder class $Ł_\a(\R)$ and $1<p<\be$, the operator belongs to $\bS_{p/\a}$, when…
Operator Hölder--Zygmund functions
A. B. Aleksandrov, V. V. Peller
It is well known that a Lipschitz function on the real line does not have to be operator Lipschitz. We show that the situation changes dramatically if we pass to Hölder classes. Na…
Lipschitz functions of perturbed operators
Fyodor Nazarov, Vladimir Peller
We prove that if is a Lipschitz function on , and are self-adjoint operators such that , then belongs to the weak space $\boldsymbol…
The behavior of functions of operators under perturbations
V. V. Peller
This is a survey article. We consider different problems in connection with the behavior of functions of operators under perturbations of operators. We deal with three classes of o…
Functions of perturbed operators
A. B. Aleksandrov, V. V. Peller
We prove that if $0<\a<1$ and is in the Hölder class $Ł_\a(\R)$, then for arbitrary self-adjoint operators and with bounded , the operator is bounded a…