Frames of subspaces for Banach spaces have been introduced and studied. Examples and
counter-examples to distinguish various types of frames of subspaces have been given. It
has been proved that if a Banach space has a Banach frame, then it also has a frame of
subspaces. Also, a necessary and sufficient condition for a sequence of projections,
associated with a frame of subspaces, to be unique has been given. Finally, we consider
complete frame of subspaces and prove that every weakly compactly generated Banach …

Bessel sequences of subspaces, frames of subspaces and independent frame of subspaces
for Banach spaces are introduced and discussed. Frames of subspaces is a generalization
of frames of subspaces for Hilbert spaces. Some necessary and sufficient conditions for a
Bessel sequence of subspaces to be a frame of subspaces for Banach spaces are given. It is
proved that a Bessel sequence of subspaces becomes a frame of subspaces for Banach
spaces if and only if its analysis operator is invertible. Lastly, Riesz bases of subspaces for …