## Linear Operators: General theory |

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Page 39

... 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

containing lo .

... 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 maximal right idealcontaining lo .

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

U2 , Uq , . . . , Uq ' g , it is

Since ...

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

U2 , Uq , . . . , Uq ' g , it is

**seen**that vg is equivalent to vg and thus that is in V .Since ...

Page 690

... it is

Pi = 1 , Pl . 31 , and T " ( t , : ) < Pn ( ( o ) ) , ) , n = 1 , 2 , . . . . By the Riesz convexity

theorem we have also P , 31 , and , since Pn = Em Pm – - 1 pm , it is

... it is

**seen**that g is in Ly . By Lemma 6 . 4 there is a positive operator Pin Ly withPi = 1 , Pl . 31 , and T " ( t , : ) < Pn ( ( o ) ) , ) , n = 1 , 2 , . . . . By the Riesz convexity

theorem we have also P , 31 , and , since Pn = Em Pm – - 1 pm , it is

**seen**from ...### What people are saying - Write a review

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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