Harmonic analysis of local operators (Q916953)

Let B be a bounded operator on some Hilbert space, \(P_ n\) the projector onto \(\ker (B^ n)\), and \(A_ n=BP_ n\). Then \(\| A^*_ nA_ n\| \leq (n-1)\| [B,B^*]\|\). A variant of this lemma is used to show that, in the framework of local relativistic field theory, the spatial Fourier transforms of local (bounded) observables form \(L^ 2\)- functions with respect to states of finite energy. This result reveals some hitherto unknown regularity properties that may prove to be useful in collision theory involving socalled infraparticles, i.e., when conventional particle interpretation fails.