Geodesic
A~lemma on approximation of finite-dimensional $*$-algebras
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part V, Tome 47 (1974), pp. 175-178

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The analogue of Glimm's lemma is proved: if the elements generating a finite-dimensional subalgebra $A$ of a finite type factor can be sufficiently well approximated by some elements of a subfactor $B$ they can also be approximated by elements of $B$ which generate an algebra isomorphic to $A$. The trace norm is used instead of the uniform one. 
@article{ZNSL_1974_47_a15,
     author = {A. A. Lodkin},
     title = {A~lemma on approximation of finite-dimensional $*$-algebras},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {175--178},
     publisher = {mathdoc},
     volume = {47},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1974_47_a15/}
}
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A. A. Lodkin. A~lemma on approximation of finite-dimensional $*$-algebras. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part V, Tome 47 (1974), pp. 175-178. http://geodesic.mathdoc.fr/item/ZNSL_1974_47_a15/