Multiplication Operators On Grand Lorentz Spaces

IŞIK G., ERYILMAZ İ.

Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi, cilt.35, sa.1, ss.42-51, 2019 (Hakemli Dergi) identifier

  • 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.