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Commutativity of compact selfadjoint operators

G. Greiner, W. Ricker (1995)

Studia Mathematica

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,...

Cyclic space isomorphism of unitary operators

Krzysztof Frączek (1997)

Studia Mathematica

We introduce a new equivalence relation between unitary operators on separable Hilbert spaces and discuss a possibility to have in each equivalence class a measure-preserving transformation.

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