Stochastics Seminar

Speaker: Dr. Jerzy Szulga

Title: Rigged Hilbert spaces, with applications to quantum operators

Abstract: All operators acting on the random discrete chaos (a.k.a. "toy Fock space") are algebraically spanned by two fundamental symmetries. They are contractions in the operator norm, yet they are not  Hilbert-Schmidt operators, albeit they are locally. The Hilbert space structure is desired, though, but seemingly is lacking. The suitably adapted classical Gelfand's construction of a "rigged Hilbert space" resolves the problem.