A model and characterization of a class of symmetric semibounded operators
Abstract
Let G be a Hilbert space, let B(G) be the algebra of bounded operators, and let ˜H=L2([0,∞);G). An operator-valued function Q∈L∞,loc([0,∞);B(G)) determines a multiplication operator in ˜H by (Qy)(x)=Q(x)y(x), x⩾0. We say that an operator L0 in a Hilbert space H is a Schr\"odinger type operator, if it is unitarily equivalent to S=−(d2/dx2)+Q, which acts in ˜H on a relevant domain. The paper provides a characterization of a class of such operators L0. The characterization is given in terms of the properties of an evolutionary dynamical system associated with L0. It is constructive: a way to realize L0 in the form of S is proposed.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Advanced Topics in Algebra
Holomorphic and Operator Theory
Publication details
- Journal / source
- Journal of Operator Theory
- Publisher
- Theta Foundation
- Volume
- 96
- Issue
- 1
- Pages
- 257–275
- Publication date
- 8 August 2026
- Language
- EN