Generalized Differentiation of a Class of Normal Cone Operators

2013 ◽  
Vol 161 (2) ◽  
pp. 398-429 ◽  
Author(s):  
Nguyen Thanh Qui
Keyword(s):  
Normal Cone ◽  
Generalized Differentiation

Proximal Normal Cone Analysis on Smooth Banach Spaces and Applications

2014 ◽  
Vol 24 (1) ◽  
pp. 363-384 ◽  
Author(s):  
Xi Yin Zheng ◽  
Kung Fu Ng
Keyword(s):  
Banach Spaces ◽  
Normal Cone ◽  
Proximal Normal Cone

scholarly journals In what spaces is every closed normal cone regular?

1970 ◽  
Vol 17 (2) ◽  
pp. 121-125 ◽  
Author(s):  
C. W. McArthur
Keyword(s):  
Banach Space ◽  
Convex Space ◽  
Unconditional Basis ◽  
Normal Cone ◽  
Closed Subspace ◽  
Locally Convex Space ◽  
Regular Part ◽  
Fréchet Space ◽  
Sequential Completeness ◽  
Locally Convex

It is known (13, p. 92) that each closed normal cone in a weakly sequentially complete locally convex space is regular and fully regular. Part of the main theorem of this paper shows that a certain amount of weak sequential completeness is necessary in order that each closed normal cone be regular. Specifically, it is shown that each closed normal cone in a Fréchet space is regular if and only if each closed subspace with an unconditional basis is weakly sequentially complete. If E is a strongly separable conjugate of a Banach space it is shown that each closed normal cone in E is fully regular. If E is a Banach space with an unconditional basis it is shown that each closed normal cone in E is fully regular if and only if E is the conjugate of a Banach space.

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