On the spectral properties of some classes of operators (Q2906284)

In this expository paper, the author considers spectral properties of operators defined by means of some order inequalities. It is shown that these operators share many spectral properties with normal operators on Hilbert spaces, mostly concerning Fredholm theory and local spectral theory. The main interest of the paper is connected with the isolated points of the spectra and of the approximate point spectra of these operators. These properties lead to the concept of polaroid operator, which with additional concepts produces a general framework from which it is stated that several versions of Weyl type theorem hold for all these operators.