Geodesic
Commutativity of compact selfadjoint operators
Studia Mathematica, Tome 112 (1994) no. 2, pp. 109-125

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The relationship between the joint spectrum γ(A) of an n-tuple $A = (A_1,..., A_n)$ of selfadjoint operators and the support of the corresponding Weyl calculus T(A) : f ↦ f(A) is discussed. It is shown that one always has γ(A) ⊂ supp (T(A)). Moreover, when the operators are compact, equality occurs if and only if the operators $A_j$ mutually commute. In the non-commuting case the equality fails badly: While γ(A) is countable, supp(T(A)) has to be an uncountable set. An example is given showing that, for non-compact operators, coincidence of γ(A) and supp (T(A)) no longer implies commutativity of the set ${A_i}$ .
DOI : 10.4064/sm-112-2-109-125

G. Greiner 1 ;  1

1 
@article{10_4064_sm_112_2_109_125,
     author = {G. Greiner and  },
     title = {Commutativity of compact selfadjoint operators},
     journal = {Studia Mathematica},
     pages = {109--125},
     publisher = {mathdoc},
     volume = {112},
     number = {2},
     year = {1994},
     doi = {10.4064/sm-112-2-109-125},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-112-2-109-125/}
}
TY  - JOUR
AU  - G. Greiner
AU  -  
TI  - Commutativity of compact selfadjoint operators
JO  - Studia Mathematica
PY  - 1994
SP  - 109
EP  - 125
VL  - 112
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-112-2-109-125/
DO  - 10.4064/sm-112-2-109-125
LA  - en
ID  - 10_4064_sm_112_2_109_125
ER  - 
%0 Journal Article
%A G. Greiner
%A  
%T Commutativity of compact selfadjoint operators
%J Studia Mathematica
%D 1994
%P 109-125
%V 112
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-112-2-109-125/
%R 10.4064/sm-112-2-109-125
%G en
%F 10_4064_sm_112_2_109_125
G. Greiner;  . Commutativity of compact selfadjoint operators. Studia Mathematica, Tome 112 (1994) no. 2, pp. 109-125. doi: 10.4064/sm-112-2-109-125

Cité par Sources :