Weyl Type Theorems for Unbounded Hyponormal Operators

Spectral Mapping Theorems for Hyponormal Operators

Let T=H+iK be hyponormal and Q be a strictly monotone increasing continuous function on s(H ). We define ~ Q(T ) by ~ Q(T )=Q(H )+iK. In this paper, we show that if z is an isolated eigenvalue of ~ Q(T ), then the corresponding Riesz projection is self-adjoint. Also we introduce Xia spectrum and study the existence of an invariant subspace of an operator ~ Q(T ).

Almost α-Hyponormal Operators with Weyl Spectrum of Area Zero

Variations of Weyl Type Theorems

A Banach space operator T satisfies property(Bgw), a variant property(gw), if the complement in the approximate point spectrum σa(T ) of the semi-B-essential approximate point spectrum σSBF− + (T ) coincides with set of isolated eigenvalues of T of finite multiplicity E(T ). We also introduce properties (Bb), and property (Bgb) in connection with Weyl type theorems, which are analogous, respect...

Polynomially hyponormal operators

A survey of the theory of k-hyponormal operators starts with the construction of a polynomially hyponormal operator which is not subnormal. This is achieved via a natural dictionary between positive functionals on specific convex cones of polynomials and linear bounded operators acting on a Hilbert space, with a distinguished cyclic vector. The class of unilateral weighted shifts provides an op...

ON p-HYPONORMAL OPERATORS

In this paper we show that p-hyponormal operators with 0 / ∈ σ(|T | 1 2 r ) are subscalar. As a corollary, we get that such operators with rich spectra have non-trivial invariant subspaces.