turkmath.org

A function $f$ continuous on the real line $\Bbb R$ is said to be operator Lipschitz if $\|f(A)-f(B)\|\leq c\, \|A-B\|$ for all self-adjoint operators $A$ and $B$, where a number $c$ depends on $f$ only. Clearly, every operator Lipschitz function $f$ satisfies the usual Lipschitz condition: $|f(x)-f(y)|\leq c\, |x-y|$ for all $x,y\in\Bbb R$. It is well known that the converse is not true. I am going to present a short introduction to the theory of operator Lipschitz functions.