Characterisation of multiplication operator on bicomplex Lorentz spaces with hyperbolic norm
MAEJO INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY, no.1, pp.1-16, 2025 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Publication Date: 2025
- Journal Name: MAEJO INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY
- Journal Indexes: 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
- Page Numbers: pp.1-16
- Ondokuz Mayıs University Affiliated: Yes
Abstract
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.