## Linear Operators: General theory |

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Page 410

A set K CX is convex if x , y eK , and o şasi , imply ax + ( 1 - a ) y e K . The

following

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 o şasi , imply ax + ( 1 - a ) y e K . The

following

**lemma**is an obvious consequence of Definition 1 . 2**LEMMA**. Theintersection of an arbitrary family of convex subsets of the linear space X is

convex .

Page 699

Q.E.D. We shall now state and prove the

reasons occurring later the following

positive sub - semi - group rather than for a positive semi - group . The proof of ...

Q.E.D. We shall now state and prove the

**lemma**referred to as CPx . For technicalreasons occurring later the following

**lemma**is stated for what might be called apositive sub - semi - group rather than for a positive semi - group . The proof of ...

Page 700

Thus , to prove the

the

Thus , to prove the

**lemma**, it will suffice to show that it is true if k is even . If k 1the

**lemma**has already been proved (**Lemma**6 ) . We shall thus suppose that the**lemma**has been proved for the integer n and shall conclude its validity for the ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

81 other sections not shown

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