Address:
Department of Mathematics, Kirori Mal College University of Delhi, Delhi 110007, India
Department of Mathematics, University of Delhi Delhi 110007, India
E-mail:
shikk2003@yahoo.co.in
vicky.h1729@gmail.com
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.