A coordinate free characterization of certain quasidiagonal operators March Boedihardjo 47A6647A58universal Banach spacesuniversal operatorsquasidiagonal operatorsultraproducts of operatorsapproximate unitary equivalenc We obtain the following: \begin{enumerate}[label=(\roman*)] \item 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, \item affirmative answers to some questions of Hadwin \item 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. \end{enumerate} Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5587 10.1512/iumj.2015.64.5587 en Indiana Univ. Math. J. 64 (2015) 515 - 531 state-of-the-art mathematics http://iumj.org/access/