A note on fusion Banach frames

S. K. Kaushik and Varinder Kumar

Department of Mathematics, Kirori Mal College University of Delhi, Delhi 110007, India
Department of Mathematics, University of Delhi Delhi 110007, India


Abstract: For a fusion Banach frame $(\lbrace G_n, v_n\rbrace , S)$ for a Banach space $E$, if $(\lbrace v_n^*(E^*), v_n^*\rbrace ,T)$ is a fusion Banach frame for $E^*$, then $(\lbrace G_n, v_n\rbrace , S; \lbrace v_n^*(E^*), v_n^*\rbrace ,T)$ is called a fusion bi-Banach frame for $E$. It is proved that if $E$ has an atomic decomposition, then $E$ also has a fusion bi-Banach frame. Also, a sufficient condition for the existence of a fusion bi-Banach frame is given. Finally, a characterization of fusion bi-Banach frames is given.

AMSclassification: primary 42C15; secondary 42A38.

Keywords: atomic decompositions, fusion Banach frames, fusion bi-Banach frames.