Dergiler / Turkish Journal of Mathematics / 2000 / Cilt: 24 - Sayı: 3
Multipliers between Orlicz Sequence Spaces
- Sayfa
- 313–319
- DOI
- —
Özet
Let M, N be Orlicz functions, and let D(\ellM , \ellN ) be the space of all diagonal operators (that is multipliers) acting between the Orlicz sequence spaces \ellM and \ellN. We prove that the space of multipliers D(\ellM , \ellN ) coincides with (and is isomorphic to) the Orlicz sequence space \ellMN* , where MN* is the Orlicz function defined by MN*(l ) = \sup \{ N(l x) - M(x), \; x \in (0,1) \}.
Abstract
Let M, N be Orlicz functions, and let D(\ellM , \ellN ) be the space of all diagonal operators (that is multipliers) acting between the Orlicz sequence spaces \ellM and \ellN. We prove that the space of multipliers D(\ellM , \ellN ) coincides with (and is isomorphic to) the Orlicz sequence space \ellMN* , where MN* is the Orlicz function defined by MN*(l ) = \sup \{ N(l x) - M(x), \; x \in (0,1) \}.