Certain invariant subspaces for operators with rich eigenvalues.
Commutativity of compact selfadjoint operators
The relationship between the joint spectrum γ(A) of an n-tuple 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 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,...
Comparison of joint spectra for certain classes of commuting operators
Concept of the spectral sets in Wachs spaces, I.
Contributi all'analisi spettrale algebrica