IJPAM: Volume 51, No. 3 (2009)
TOWARDS THE SPECTRUM
Department of Mathematics
P.O. Box 333, Maseno, KENYA
Abstract.A closed densely defined operator , on a Banach space X, whose spectrum is contained in R and satisfies
Examples of such operators include self-adjoint operators, Laplacian on , Schrödinger operators on and operators whose spectra lie in R and permit some control on e^iHt.
In this paper we will characterise the
operators. In particular we show that property () is stable under dialation by real numbers in the interval (0,1) and perturbation by positive reals. We will also show that is is of then so is .
Received: March 13, 2008
AMS Subject Classification: 47A10
Key Words and Phrases: spectrum, resolvent, eigenvalues, diagonalizable, scale invariant
Source: International Journal of Pure and Applied Mathematics