On the Lie-Trotter theorems inL p -spaces |
| |
Authors: | Yu. A. Semenov |
| |
Affiliation: | 1. Kiev Polytechnic Institute, Kiev, U.S.S.R.
|
| |
Abstract: | In this paper we consider operatorsH 0 andV possessing the following properties: - H 0 is a positive self-adjoint operator acting inL 2(M, γ) with γ a probability measure, so that exp(?tH 0) is a contraction onL 1(M, γ) for eacht>0.
- V is a semibounded multiplicative operator acting inL 2(M, γ) {fx379-1}
Under these assumptions theorems of Lie-Trotter type are derived for the operatorsH, H 0, V, whereH is a self-adjoint extension of the algebraic sumH 0+V, and is built by the form method. Under the additional assumption thatV(·)∈L 2(M, γ) we prove an essential self-adjointness ofH 0+V. The results obtained are applicable to non-relativistic quantum mechanics. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|