## Linear Operators: General theory |

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Page 410

1 DEFINITION . A

K . The following lemma is an obvious consequence of Definition 1 . 2 LEMMA .

The intersection of an arbitrary family of

1 DEFINITION . A

**set**K CX is**convex**if x , y eK , and o şasi , imply ax + ( 1 - 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 ...Page 410

1 DEFINITION . A

y e K. The following lemma is an obvious consequence of Definition 1 . 2 LEMMA

. The intersection of an arbitrary family of

...

1 DEFINITION . A

**set**K CX is**convex**if x , y € K , and 0 sa si , 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...

Page 461

and an arbitrary

Theorem 2 . 8 ) . He also proved that a

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 ( compareTheorem 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

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

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