University of Western Australia, Nedlands, WA. Fiona R Lake, MD, FRACP, Associate Professor in Medicine and Medical Education, Education Centre, Faculty of Medicine and Dentistry; Jeffrey M Hamdorf, PhD, FRACS, Associate Professor in Surgical Education, School of Surgery and Pathology. Reprints will not be available from the authors. Correspondence: Associate Professor Fiona R Lake, Education C...

In this article, we characterize absolutely norm attaining normal operators in terms of the essential spectrum. Later prove a structure theorem for hyponormal (or AN -operators short) and deduce conditions normality operator.

Abstract In this article, we provide necessary and sufficient conditions for the existence of non-norm-attaining operators in $\mathcal {L}(E, F)$ . By using a theorem due to Pfitzner on James boundaries, show that if there exists relatively compact set K (in weak operator topology) such $0$ is an element its closure but it not norm-closed convex hull, then can guarantee does attain norm. This ...