- Tytuł:
- Commutativity of compact selfadjoint operators
- Autorzy:
-
Greiner, G.
Ricker, W. - Powiązania:
- https://bibliotekanauki.pl/articles/1289918.pdf
- Data publikacji:
- 1995
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- 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 ${A_i}$ .
- Źródło:
-
Studia Mathematica; 1994-1995, 112, 2; 109-125
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł