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

Authors

  • S. K. Kaushik Department of Mathematics, Kirori Mal College, University of Delhi, Delhi 110007
  • Varinder Kumar Department of Mathematics, Shaheed Bhagat Singh College, University of Delhi, Delhi 110017

DOI:

https://doi.org/10.26713/cma.v3i3.214

Keywords:

Frame, Banach frame, Fusion Banach frame, Atomic decomposition

Abstract

$\mathcal{AD}$-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.

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How to Cite

Kaushik, S. K., & Kumar, V. (2012). $\mathcal{AD}$-Frames satisfying Property $\mathcal{B}$. Communications in Mathematics and Applications, 3(3), 303–312. https://doi.org/10.26713/cma.v3i3.214

Issue

Vol. 3 No. 3 (2012)

Section

Research Article

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