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Quasi-Differentiable Norms

Published online by Cambridge University Press:  20 November 2018

J. H. M. Whitfield
J. H. M. Whitfield*
Affiliation:
Lakehead University
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Let E be a real Banach space with norm ρ. Let S={x ∊ E: ρ(x) = 1}. A norm on E is admissible if it generates the same topology as ρ.

The normρ is Gateaux differ-entiable if for each x ∊ S and u ∊ E

exists.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 3 , 01 September 1974 , pp. 407 - 408
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Bonic, R. and Frampton, J., Smooth functions on Banach manifolds, J. Math. Mech. 15 (1966), 877-898.Google Scholar
2. Cudia, D. F., The geometry of Banach spaces. Smoothness, Trans. Amer. Math. Soc. 110 (1964), 284-314.Google Scholar
3. Day, M. M., Normed Linear Spaces, Academic Press, New York, 1962. (1964), 284-314.Google Scholar
4. Goodman, V., Quasi-differentiable functions on Banach spaces, Proc. Amer. Math. Soc. 30 (1971), 367-370.Google Scholar