The notion of J-frames in Banach spaces has been defined and studied. A necessary and
sufficient condition for the existence of a J-frame in a Banach space has been given. Also, a
sufficient condition, in terms of J-frame, the existence of bounded approximation property in
a Banach space has been given. Further, we study the interplay between the existence of
retro Banach frames in conjugate Banach spaces and the existence of a support cone.
Finally, we have given conditions for the existence of a retro Banach frame in the conjugate …