Completeness of Sums of Subspace of Bounded Functions and Applications

Abstract

We give a new proof of a characterization of the closeness of the range of a continuous linear operator and of the closeness of the sum of two closed vector subspaces of a Banach space. Then we state sufficient conditions for the closeness of the sum of two closed subspaces of the Banach space of bounded functions and apply this result on various pseudo almost periodic spaces and pseudo almost automorphic spaces.

References in corpus (2)

• On completeness of the space of weighted pseudo almost automorphic functions
• A note on closedness of the sum of two closed subspaces in a Banach space

Cited by in corpus (1)

• Stepanov pseudo almost periodic functions and applications