$\mathcal{AD}$-Frames satisfying Property $\mathcal{B}$

S. K. Kaushik, Varinder Kumar


$\mathcal{AD}$-frames in Banach spaces have been introduced and studied. Some necessary conditions for existence of $\mathcal{AD}$-frames have been given. Property $\mathcal{B}$ for $\mathcal{AD}$-frames is defined and a characterization of $\mathcal{AD}$-frames satisfying property $\mathcal{B}$ has been obtained. Also, we gave a sufficient condition for an $\mathcal{AD}$-frame to satisfy property $\mathcal{B}$ and a necessary condition for a particular type of $\mathcal{AD}$-frame satisfying property $\mathcal{B}$. Finally, a result regarding quasi-reflexivity of Banach spaces having $\mathcal{AD}$-frames satisfying property $\mathcal{B}$ is proved.


Frame; Banach frame; Fusion Banach frame; Atomic decomposition

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DOI: http://dx.doi.org/10.26713%2Fcma.v3i3.214


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