Linear Operators: General theory |
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Page 410
A set K Q X is convex ifx,ye K, and 0 ^ a ^ 1, imply ax-\-(l — a)y e K. The following lemma is an obvious consequence of Definition 1. 2 Lemma. The intersection of an arbitrary family of convex subsets of the linear space X is convex.
A set K Q X is convex ifx,ye K, and 0 ^ a ^ 1, imply ax-\-(l — a)y e K. The following lemma is an obvious consequence of Definition 1. 2 Lemma. The intersection of an arbitrary family of convex subsets of the linear space X is convex.
Page 410
A set K CX is convex if x , y eK , and 0 sa s 1 , imply ax + ( 1 - aly e K. The following lemma is an obvious consequence of Definition 1 . 2 LEMMA . The intersection of an arbitrary family of convex subsets of the linear space X is ...
A set K CX is convex if x , y eK , and 0 sa s 1 , imply ax + ( 1 - aly e K. The following lemma is an obvious consequence of Definition 1 . 2 LEMMA . The intersection of an arbitrary family of convex subsets of the linear space X is ...
Page 461
and an arbitrary convex set is possible , provided they are disjoint ( compare Theorem 2.8 ) . He also proved that a convex set K which is compact in the X * topology of the normed linear space X , can be separated from an arbitrary ...
and an arbitrary convex set is possible , provided they are disjoint ( compare Theorem 2.8 ) . He also proved that a convex set K which is compact in the X * topology of the normed linear space X , can be separated from an arbitrary ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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