## Linear Operators, Part 1 |

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Page 169

5 Show that ( i ) , ( ii ) , and ( iii ) of Theorem 3.6 imply that f is in L , ( S , E , \ ) and

that in - f , converges to

bounded . Suppose that the field Eis separable under the metric g ( E , F ) = v ( u

...

5 Show that ( i ) , ( ii ) , and ( iii ) of Theorem 3.6 imply that f is in L , ( S , E , \ ) and

that in - f , converges to

**zero**even if { / n } is a generalized sequence . 6 Let u bebounded . Suppose that the field Eis separable under the metric g ( E , F ) = v ( u

...

Page 204

a , ( ds ) does not converge to

dominated convergence theorem ( 6.16 ) that there is a point in Sa for which In (

sq ) is defined for all n and for which the sequence { fn ( $ & ) } does not converge

to ...

a , ( ds ) does not converge to

**zero**and since 0 < In ( sa ) si it follows from thedominated convergence theorem ( 6.16 ) that there is a point in Sa for which In (

sq ) is defined for all n and for which the sequence { fn ( $ & ) } does not converge

to ...

Page 557

In the same way , there exist non -

) x ; = 0 . If R = S : S ... Sx , then R ( T ) x ; = 0 , and consequently R ( T ) x = 0 for

all x e X. Thus a non -

...

In the same way , there exist non -

**zero**polynomials Si , i = 2 , ... , k such that S ( T) x ; = 0 . If R = S : S ... Sx , then R ( T ) x ; = 0 , and consequently R ( T ) x = 0 for

all x e X. Thus a non -

**zero**polynomial R exists such that R ( T ) Let R be factored...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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