A coordinate free characterization of certain quasidiagonal operators

We obtain (i) a new, coordinate free, characterization of quasidiagonal operators with essential spectra contained in the unit circle by adapting the proof of a classical result in the theory of Banach spaces, (ii) an affirmative answer to some questions of Hadwin, and (iii) an alternative proof of Hadwin's characterization of the SOT, WOT and $*$-SOT closure of the unitary orbit of a given operator on a separable, infinite dimensional, complex Hilbert space

ON MEAN ERGODIC CONVERGENCE IN THE CALKIN ALGEBRAS

(Communicated by) Abstract. In this paper, we give a geometric characterization of mean ergodic convergence in the Calkin algebras for Banach spaces that have the bounded compact approximation property. 1