Spectral mapping theorem and Weyl's theorem for (m, n)-paranormal operators


Preeti Dharmarha, Sonu Ram




In the present paper, we prove spectral mapping theorem for (m, n)-paranormal operator T on a separable Hilbert space, that is, f (σ w (T)) = σ w (f (T)) when f is an analytic function on some open neighborhood of σ(T). We also show that for (m, n)-paranormal operator T, Weyl's theorem holds, that is, σ(T) − σ w (T) = π 00 (T). Moreover, if T is algebraically (m, n)-paranormal, then spectral mapping theorem and Weyl's theorem hold