Kato-Rellich theorem

Let be a Hilbert spaceMathworldPlanetmath, A:D(A) a self-adjoint operator and B:D(B) a symmetric operator with D(A)D(B).

We say that B is A-bounded if there are positive constants α,β such that


for all xD(A), and we say that α is an A-bound for B.

Theorem 1.

(Kato-Rellich) If B is A-bounded with A-bound smaller than 1, then A+B is self-adjointPlanetmathPlanetmath on D(A), and essentially self-adjoint on any core of A. Moreover, if A is bounded below, then so is A+B.

Title Kato-Rellich theorem
Canonical name KatoRellichTheorem
Date of creation 2013-03-22 14:52:59
Last modified on 2013-03-22 14:52:59
Owner Koro (127)
Last modified by Koro (127)
Numerical id 7
Author Koro (127)
Entry type Theorem
Classification msc 47A55
Synonym Rellich-Kato theorem
Defines A-bounded
Defines A-bound