Commutativity of compact selfadjoint operators
Greiner, G. ; Ricker, W.
Studia Mathematica, Tome 113 (1995), p. 109-125 / Harvested from The Polish Digital Mathematics Library
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The relationship between the joint spectrum γ(A) of an n-tuple A=(A1,...,An) 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 Aj 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 Ai .

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:216141 
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Greiner, G.; Ricker, W. Commutativity of compact selfadjoint operators. Studia Mathematica, Tome 113 (1995) pp. 109-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv112i2p109bwm/

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