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Characterisation of multiplication operator on bicomplex Lorentz spaces with hyperbolic norm |
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| รหัสดีโอไอ | |
| Creator | Ilker Eryilmaz |
| Title | Characterisation of multiplication operator on bicomplex Lorentz spaces with hyperbolic norm |
| Publisher | Maejo University |
| Publication Year | 2568 |
| Journal Title | Maejo International Journal of Science and Technology |
| Journal Vol. | 19 |
| Journal No. | 1 |
| Page no. | 1 |
| Keyword | bicomplex numbers, BC-valued functions, hyperbolic norm, D-distribution function, D-rearrangement, multiplication operator, Fredholm operator |
| Website title | Maejo International Journal of Science and Technology |
| ISSN | 1905-7873 |
| Abstract | The multiplication operator Mu f=u.f within the bicomplex Lorentz space L(p,q)BC( ,M, ) is investigated. It is initially established that Mu is D-bounded if and only if the function u is essentially D-bounded. Subsequently, it is proved that the collection of all D-bounded multiplication operators on BC-Lorentz spaces forms a maximal abelian sub-algebra within the Banach algebra of all bounded linear operators on L(p,q)BC ( ,M, ). Additionally, a necessary and sufficient condition for the compactness of Mu is provided. Finally, by introducing a condition for a multiplication operator to exhibit a closed range, the author identifies some conditions equivalent to Mu being a Fredholm operator. |
