Weyl's theorem for algebraically \(wF(p, r, q)\) operators with \(p, r > 0\) and \(q \geq 1\)
The author shows that, if an operator \(T\) or its adjoint \(T^{*}\) acting in an infinite-dimensional separable Hilbert space is algebraically \(wF(p,r,q)\) with \(p,r>0\) and \(q\geqslant 1\), then \(f(T)\) satisfies Weyl's theorem for any analytic function \(f\) in an open neighborhood of the spectrum \(\sigma(T)\) of \(T\). The spectral mapping theorem for the Weyl spectrum of \(T\) and for the essential approximate spectrum of \(T\) is established for any analytic function in an open neighborhood of the spectrum of \(T\).
scientific article; zbMATH DE number 6110026
scientific article