scholarly journals Smooth functions and partitions of unity on certain Banach spaces

1996 ◽  
Vol 47 (188) ◽  
pp. 455-468 ◽  
Author(s):  
R Haydon
Keyword(s):  
Banach Spaces ◽  
Smooth Functions

scholarly journals Duals of Banach spaces which admit nontrivial smooth functions

1974 ◽  
Vol 11 (2) ◽  
pp. 161-166 ◽  
Author(s):  
K. John ◽  
V. Zizler
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Differentiable Function ◽  
Continuous Linear ◽  
Smooth Functions ◽  
One To One ◽  
Fréchet Differentiable

If a Banach space X admits a continuously Fréchet differentiable function with bounded nonempty support, then X* admits a projectional resolution of identity and a continuous linear one-to-one map into co(Γ).

scholarly journals Approximation by functions with bounded derivative on Banach spaces

2004 ◽  
Vol 69 (1) ◽  
pp. 125-131 ◽  
Author(s):  
R. Fry
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Open Subset ◽  
Separable Banach Space ◽  
Smooth Functions ◽  
Continuous Map ◽  
Smooth Norm ◽  
Uniformly Continuous ◽  
Bounded Derivative

Let X be a separable Banach space which admits a C1-smooth norm, and let G ⊂ X be an open subset. Then any real-valued, bounded and uniformly continuous map on G can be uniformly approximated on G by C1-smooth functions with bounded derivative.

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