Abstract
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 Banach spaces are introduced. It is shown that an independent frame of subspaces is just a Riesz Basis for Banach spaces.KeywordsFrame of subspacesRiesz basis of subspacesBanach space
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