Multiplication operators in variable Lebesgue spaces

Abstract

In this note we will characterize the boundedness, invertibility, compactness and closedness of the range of multiplication operators on variable Lebesgue spaces.

Multiplication Operators on Second Order Cesaro-Orlicz Sequence Spaces

“…Mursaleen et al [4], ˙Ilkhan et al [5] have studied multiplication operators on Cesàro function spaces. Further, Castillo et al [6][7][8], obtained significant results and modified the techniques used by the others to study multiplication operators on Orlicz-Lorentz spaces, weak L p spaces and variable Lebesgue spaces.…”

Multiplication operators on the space of functions of bounded variation

“…The properties of the multiplication operator on measurable function spaces have been studied by numerous mathematicians. It is worth referring to the outstanding works of Abrahamese [6], Halmos [7], Takagi and Yokouchi [8] and Castillo, Rafeiro and Ramos-Ferández [9]. Recently, Castillo, Ramos-Fernández and SalasBrown [5] made a very comprehensive study about the properties of Mu acting on Köthe spaces.…”

On the Essential Norm of Multiplications Operators Acting on Cesàro Sequence Spaces

“…Additionally, we note that the work of Arora et al in [4][5][6] examined properties of on Lorentz and Lorentz-Bochner spaces. Further significant results regarding multiplication operators were obtained by Castillo et al in [7][8][9], in which these authors showed that the techniques used by previously mentioned authors can be modified to study multiplication operators on weak spaces, Orlicz-Lorentz spaces, and variable Lebesgue spaces.…”