A Note on Generalized Multiplier Spaces and Applications to $\alpha AB$-, $\beta AB$-, $\gamma AB$- and $NAB$-duals

Ivana Djolovic, Davoud Foroutannia, Hadi Roopaei


We will start with the set $M(X,Y)$, multiplier space, defined by:


M(X,Y)=\{a=(a_k)\in \omega \mid ax\in Y \mbox{, for all }x\in X\}


where $\omega$ denotes the space of all complex-valued sequences and $X$ and $Y$ are sequence spaces. Specially, putting $Y=cs$, where $cs$ is the set of convergent series, the multiplier space becomes the $\beta$-dual of $X$. We will present some generalized results related to $X^{\beta}$ and extend some of existing. Finally, we will illustrate these generalizations with some examples and applications.

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