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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. LOMI, 1974 Volume 47, Pages 175–178 (Mi znsl2778)

Short communications

A lemma on approximation of finite-dimensional $*$-algebras

A. A. Lodkin


Abstract: 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.

UDC: 513.88



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