## Linear Operators: General theory |

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Results 1-3 of 82

Page 61

( i ) and ( ii ) are satisfied , Lemma 3 shows that the hypotheses of Theorem 1 . 18

are satisfied . From that theorem it is

continuous . Thus Lemma 4 shows that T is bounded . Now , when Tx exists , Tx ...

( i ) and ( ii ) are satisfied , Lemma 3 shows that the hypotheses of Theorem 1 . 18

are satisfied . From that theorem it is

**seen**that Tx exists for each X , and that T iscontinuous . Thus Lemma 4 shows that T is bounded . Now , when Tx exists , Tx ...

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 V

2 , Uq , . . . , Uq ' , Vg , 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 V

2 , Uq , . . . , Uq ' , Vg , it is

**seen**that ug is equivalent to v g , and thus that vp is inV ...

Page 449

Let B , be the dense subset of the boundary B of A at which there are non - zero

functionals tangent to A . We have

. Since aA , + ( 1 - a ) A is open , ( aA , + ( 1 - a ) A ) n B = $ for 0 < a < 1 . Let pe A

...

Let B , be the dense subset of the boundary B of A at which there are non - zero

functionals tangent to A . We have

**seen**that ( aA , + ( 1 - a ) A ) B = $ for 0 < a < 1. Since aA , + ( 1 - a ) A is open , ( aA , + ( 1 - a ) A ) n B = $ for 0 < a < 1 . Let pe A

...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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