When strict singularity of operators coincides with weak compactness

Pascal Lefèvre (1)

1 LML - Laboratoire de Mathématiques de Lens

We prove that the notions of finite strict singularity, strict singularity and weak compactness coincide for operators defined on various spaces: the disc algebra, subspaces of C(K) with reflexive annihilator and subspaces of the Morse-Transue-Orlicz space $M^{\psi_q} (\Omega;\mu )$ with q > 2.

Mots clés: finitely strictly singular operators; Weak compactness; strictly singular operators; finitely strictly singular operators.

Domaines: Analyse fonctionnelle [math.FA]

Pascal Lefèvre. When strict singularity of operators coincides with weak compactness. Journal of Operator Theory, 2012, 67 (2), pp.101-110. ⟨hal-00766028⟩