Extended Spectrum, Extended Eigenspaces and Normal Operators

Gilles Cassier (1) , Hasan Alkanjo (1)

1 EDPA - Équations aux dérivées partielles, analyse

We say that a complex number λ is an extended eigenvalue of a bounded linear operator T on a Hilbert space H if there exists a nonzero bounded linear operator X acting on H, called extended eigen- vector associated to λ, and satisfying the equation T X = λXT . In this paper we describe the sets of extended eigenvalues and extended eigen- vectors for the product of a positive and a self-adjoint operator which are both injective. We also treat the case of normal operators.

Mots clés: Extended eigenvalues Extended eigenspaces Normal operators Product of a positive operator by a self-adjoint one

Domaines: Analyse fonctionnelle [math.FA]

Gilles Cassier, Hasan Alkanjo. Extended Spectrum, Extended Eigenspaces and Normal Operators. Journal of Mathematical Analysis and Applications, 2014, 418 (Issue 1), pp.305-316. ⟨hal-00864578⟩