Geodesic
Operator noncommutative functions
Canadian mathematical bulletin, Tome 66 (2023) no. 2, pp. 492-508

Voir la notice de l'article provenant de la source Cambridge

DOI

We establish a theory of noncommutative (NC) functions on a class of von Neumann algebras with a particular direct sum property, e.g., $B({\mathcal H})$. In contrast to the theory’s origins, we do not rely on appealing to results from the matricial case. We prove that the $k{\mathrm {th}}$ directional derivative of any NC function at a scalar point is a k-linear homogeneous polynomial in its directions. Consequences include the fact that NC functions defined on domains containing scalar points can be uniformly approximated by free polynomials as well as realization formulas for NC functions bounded on particular sets, e.g., the NC polydisk and NC row ball.
DOI : 10.4153/S0008439522000339
Mots-clés : NC functions, free analysis, free polynomials, operator-valued functions 
Augat, Meric; McCarthy, John E. Operator noncommutative functions. Canadian mathematical bulletin, Tome 66 (2023) no. 2, pp. 492-508. doi: 10.4153/S0008439522000339
@article{10_4153_S0008439522000339,
     author = {Augat, Meric and McCarthy, John E.},
     title = {Operator noncommutative functions},
     journal = {Canadian mathematical bulletin},
     pages = {492--508},
     year = {2023},
     volume = {66},
     number = {2},
     doi = {10.4153/S0008439522000339},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000339/}
}
TY  - JOUR
AU  - Augat, Meric
AU  - McCarthy, John E.
TI  - Operator noncommutative functions
JO  - Canadian mathematical bulletin
PY  - 2023
SP  - 492
EP  - 508
VL  - 66
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000339/
DO  - 10.4153/S0008439522000339
ID  - 10_4153_S0008439522000339
ER  - 
%0 Journal Article
%A Augat, Meric
%A McCarthy, John E.
%T Operator noncommutative functions
%J Canadian mathematical bulletin
%D 2023
%P 492-508
%V 66
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000339/
%R 10.4153/S0008439522000339
%F 10_4153_S0008439522000339

Cité par Sources :