Geodesic
Commutativity of compact selfadjoint operators
Studia Mathematica, Tome 112 (1994) no. 2, pp. 109-125 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 ${A_i}$ . 
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     author = {G. Greiner and  },
     title = {Commutativity of compact selfadjoint operators},
     journal = {Studia Mathematica},
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     language = {en},
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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

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