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Locally flat Banach spaces

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Abstract

The notion of functions dependent locally on finitely many coordinates plays an important role in the theory of smoothness and renormings on Banach spaces, especially when higher order smoothness is involved. In this note we investigate the structural properties of Banach spaces admitting (arbitrary) bump functions depending locally on finitely many coordinates.

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Authors and Affiliations

  1. Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Michal Johanis

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  1. Michal Johanis
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Correspondence to Michal Johanis.

Additional information

This work was supported by the research project MSM 0021620839 and by the grant of the Grant Agency of the Czech Republic No. 201/05/P582 and No. 201/06/0018.

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Johanis, M. Locally flat Banach spaces. Czech Math J 59, 273–284 (2009). https://doi.org/10.1007/s10587-009-0019-1

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  • DOI: https://doi.org/10.1007/s10587-009-0019-1

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