Multiplication operators on non-commutative spaces

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 pspaces and a partial solution obtained in the more general setting of quantum Orlicz spaces.

Banach Lattice Structures and Concavifications in Banach Spaces

“…The norm g M(X(µ),Y(µ)) for a function g in this space if given by the operator norm of M g . Many papers have been written on spaces of multiplication operators; for a current review see, for example, [20]; also see [21] for an extension of this notion to the setting of non-commutative spaces.…”

Noncommutative Yosida–Hewitt theorem in noncommutative Calderón–Lozanovskiĭ spaces

“…It is clear that E × (M) = E(M) × = M(E(M), L 1 (M)) (see [12]). We refer to [12,13] for more details on such spaces. Definition 2 For Orlicz function and symmetric space E, we define the noncommutative Calderón-Lozanovskiĭ space E (M) by where the functional…”

“…(ii) Let E = L 1 and let be a convex Orlicz function. Then E (M) = L (M) is a noncommutative Orlicz space, so it is a Banach space with Fatou property (see [2,13,17] for more information about noncommutative Orlicz spaces).…”