Characterisation of multiplication operator on bicomplex Lorentz spaces with hyperbolic norm

Eryılmaz İ.

MAEJO INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY, sa.1, ss.1-16, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Dergi Adı: MAEJO INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Agricultural & Environmental Science Database, Aqualine, Aquatic Science & Fisheries Abstracts (ASFA), CAB Abstracts, Communication Abstracts, Metadex, Veterinary Science Database, Directory of Open Access Journals, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1-16
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

The multiplication operator M (u) f = u. f within the bicomplex Lorentz space L-p,L-q (BC) (Omega, R, theta), is investigated. It is initially established that M-u is D-bounded if and only if the function u is essentially D-bounded. Subsequently, it is proved that the collection of all Dbounded multiplication operators on BC-Lorentz spaces forms a maximal abelian sub-algebra within the Banach algebra of all bounded linear operators on L-p,L-q (BC) (Omega, R, theta). Additionally, a necessary and sufficient condition for the compactness of M-u is provided. Finally, by introducing a condition for a multiplication operator to exhibit a closed range, the author identifies some conditions equivalent to M-u being a Fredholm operator.