Multiplication operators on non-commutative spaces

Pierre de Jager; Louis Labuschagne

doi:10.1016/j.jmaa.2019.03.001

paper

Multiplication operators on non-commutative spaces

arXiv:1811.00269 · doi:10.1016/j.jmaa.2019.03.001

Abstract

Boundedness and compactness properties of multiplication operators on quantum (non-commutative) function spaces are investigated. For endomorphic multiplication operators these properties can be characterized in the setting of quantum symmetric spaces. For non-endomorphic multiplication operators these properties can be completely characterized in the setting of quantum $L^{p}$ -spaces and a partial solution obtained in the more general setting of quantum Orlicz spaces.