EXTENDED SPECTRUM AND EXTENDED EIGENSPACES OF QUASI-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 eigenvalueof a bounded linear operator T on a Hilbert space H if there exists anonzero bounded linear operator X acting on H, called extended eigen-vector associated to λ, and satisfying the equation T X = λXT . In thispaper we describe the sets of extended eigenvalues and extended eigen-vectors for the product of a positive and a self-adjoint operator whichare both injective. We also treat the case of normal operators.

Mots clés: subnormal operators; Intertwining values; Extended Eigenvalues; quasi-normal operators.; λ-intertwining operators; Extended Eigenspaces; normal operators

Domaines: Analyse fonctionnelle [math.FA]

Gilles Cassier, Hasan Alkanjo. EXTENDED SPECTRUM AND EXTENDED EIGENSPACES OF QUASI-NORMAL OPERATORS. Banach Journal of Mathematical Analysis, 2017, Volume 11 (Number 2), pp.266-281. ⟨hal-01175460v2⟩