Geodesic
Stability under Small Hilbert-Schmidt Perturbations for $C^*$-Algebras
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 3, pp. 92-97

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper studies the tracial stability of $C^*$-algebras, which is a general property of stability of relations in a Hilbert–Schmidt-type norm defined by a trace on a $C^*$-algebra. Precise definitions are formulated in terms of tracial ultraproducts. For nuclear $C^*$-algebras, a characterization of matricial tracial stability in terms of approximation of tracial states by traces of finite-dimensional representations is obtained. For the nonnuclear case, new obstructions and counterexamples are constructed in terms of free entropy theory.
Keywords: tracial ultraproduct, tracial stability, tracial norms, almost commuting matrices. 
@article{FAA_2018_52_3_a9,
     author = {D. Hadwin and T. V. Shulman},
     title = {Stability under {Small} {Hilbert-Schmidt} {Perturbations} for $C^*${-Algebras}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {92--97},
     publisher = {mathdoc},
     volume = {52},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2018_52_3_a9/}
}
TY  - JOUR
AU  - D. Hadwin
AU  - T. V. Shulman
TI  - Stability under Small Hilbert-Schmidt Perturbations for $C^*$-Algebras
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2018
SP  - 92
EP  - 97
VL  - 52
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2018_52_3_a9/
LA  - ru
ID  - FAA_2018_52_3_a9
ER  - 
%0 Journal Article
%A D. Hadwin
%A T. V. Shulman
%T Stability under Small Hilbert-Schmidt Perturbations for $C^*$-Algebras
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2018
%P 92-97
%V 52
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2018_52_3_a9/
%G ru
%F FAA_2018_52_3_a9
D. Hadwin; T. V. Shulman. Stability under Small Hilbert-Schmidt Perturbations for $C^*$-Algebras. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 3, pp. 92-97. http://geodesic.mathdoc.fr/item/FAA_2018_52_3_a9/