## Linear Operators: General theory |

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Page 39

Let & be ordered by C ; if F is a totally ordered subsystem of E , then it is easy to

see that UF is a right ideal in R which does not contain e . Zorn's lemma ( 2.7 )

applies to give a maximal element in E , which is readily

right ...

Let & be ordered by C ; if F is a totally ordered subsystem of E , then it is easy to

see that UF is a right ideal in R which does not contain e . Zorn's lemma ( 2.7 )

applies to give a maximal element in E , which is readily

**seen**to be a maximalright ...

Page 254

Now since uge U there is a finite chain of the form given in ( * ) above in which

successive vectors have non - zero scalar products . Thus by forming the chain

UB , Uq , ... , Ug's 0 g , it is

V.

Now since uge U there is a finite chain of the form given in ( * ) above in which

successive vectors have non - zero scalar products . Thus by forming the chain

UB , Uq , ... , Ug's 0 g , it is

**seen**that vp is equivalent to vge and thus that vp is inV.

Page 690

d ] " = Ssds so 17 ( t ) ( 4,8 ) | ” dt = So 17 ( t ) } dt = \ / \ % . it is

By Lemma 6.4 there is a positive operator P in L , with P , S1 , Plo S1 , and \ T " ( t

, :) SP " ( 11 ( • ) ) , :) , n = 1 , 2 , . . .. By the Riesz convexity theorem we have ...

d ] " = Ssds so 17 ( t ) ( 4,8 ) | ” dt = So 17 ( t ) } dt = \ / \ % . it is

**seen**that g is in Ly .By Lemma 6.4 there is a positive operator P in L , with P , S1 , Plo S1 , and \ T " ( t

, :) SP " ( 11 ( • ) ) , :) , n = 1 , 2 , . . .. By the Riesz convexity theorem we have ...

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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