A source of counterexamples in operator theory and how to construct them

Abstract

It is known that the function ƒ(t) = |t| fails to satisfy an “operator Lipschitz condition,” in the sense that the best bound upon ‖|A| − |B|‖ ‖A − B‖ infinity with the dimensionality of the (finite-dimensional Hilbert) space where A and B act. Two new ways of supplying the counterexamples are given here, to exemplify an approach that is believed to have wider applicability.