Multiplication Operators On Grand Lorentz Spaces


Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol.35, no.1, pp.42-51, 2019 (Peer-Reviewed Journal) identifier


Let( X, ,  )be a -finite measure space,fbe a complex-valuedmeasurable function defined onXandu X: →be a measurable function suchthatu f M   ( X,)wheneverf M ( X,)whereM ( X,)is the set of allmeasurable functions defined onX. This gives rise to a linear transformation: ( , , ) ( ) M M MuX X  → defined by( ) = u M f fu, where the product offunctions is pointwise. In case ifM ( X,)is a topological vector space andMuisa continuous (bounded) operator, then it is called a multiplication operator inducedbyu . In this paper, multiplication operators on grand Lorentz spaces are definedand the fundamental properties such as boundedness, closed range, invertibility,compactness and closedness of these are characterized.