Multiplication Operators On Grand Lorentz Spaces
Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi, cilt.35, sa.1, ss.42-51, 2019 (TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 35 Sayı: 1
- Basım Tarihi: 2019
- Dergi Adı: Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.42-51
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
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.