Linear Operators: General theory |
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Page 410
A set K Q X is convex iix,ye K, and 0 52 a 52 1, imply ax-\-(\—a)y eK. 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 iix,ye K, and 0 52 a 52 1, imply ax-\-(\—a)y eK. 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 Sasi , imply ax + ( 1 - 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 CX is convex if x , y eK , and 0 Sasi , imply ax + ( 1 - 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 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
closed ...
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
closed ...
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Contents
Metric Spaces | 19 |
Convergence and Uniform Convergence of Generalized | 26 |
Exercises | 33 |
Copyright | |
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