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FRAMES OF SUBSPACES FOR BANACH SPACES

https://doi.org/10.1142/S0219691310003481Cited by:6 (Source: Crossref)

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 space has a complete frame of subspaces.

An erratum has been published. .

AMSC: 42C15, 42C40