This is an announcement for the paper "The spectrum of operators on C(K) with the Grothendieck Property and characterization of J-class operators which are adjoints" by Amir Bahman Nasseri.
Abstract: This article deals with properties of spectra of operators on C(K)-spaces with the Grothendieck property (e.g. l^{\infty}) and application to so called J-class operators introduced by A. Manoussos and G. Costakis. We will show that C(K) has the Grothendieck property if and only if the boundary of the spectrum of every operator on C(K) consists entirely of eigenvalues of its adjoint. As a consequence we will see that there does not exist invertible J-class operators on C(K) with the Grothendieck property. In the third section we will give a quantitative and qualitative characterization of all J-class operators on l^{\infty} which are adjoints from operators on l^1.
Archive classification: math.SP math.DS math.FA
Remarks: 19 pages
Submitted from: nasseri@uni-wuppertal.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.3815
or