ABSTRACT
In his famous paper H. Weyl proved that for a hermitian operator defined on a Hilbert space the set of limits points in the spectrum (a point in the spectrum of a hermitian operator is called a limit point if it is an eigenvalue of infinite multiplicity) remains invariant under compact hermitian perturbations. This very elegant result was extended to more general classes of operators. The first result in this direction was obtained by Coburn (1965), for the case of hyponormal operators and for a class of Toeplitz operators. The extension to certain classes of operators satisfying a growth condition was obtained in Istrǎţescu (1968). In Schechter (1970) and Berberian (1969) these results are extended further to larger classes of operators. All of these results were obtained using some results of Schechter (1970). In his paper Schechter (1970) extends the results to more general operators and also results for the case of Banach space operators. Related results for some sorts of essential spectra were obtained by several authors.
