Journal of Operator Theory

Volume 67, Issue 2, Spring 2012 pp. 369-378.

When strict singularity of operators coincides with weak compactness

Authors: Pascal Lefevre
Author institution: Univ Lille Nord de France, U-Artois, Laboratoire de Mathematiques de Lens EA 2462, Federation CNRS Nord-Pas-de-Calais FR 2956, F-62 300 Lens, France

Summary: 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 $q>2$.

Keywords: weak compactness, strictly singular operators, finitely strictly singular operators

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