## Linear Operators, Part 1 |

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Page 403

It

measure defined intrinsically in any n - dimensional real Hilbert space H , without

reference to any particular coordinate system in that space . This measure will be

...

It

**follows**from the rotational invariance of un that Un may be regarded as ameasure defined intrinsically in any n - dimensional real Hilbert space H , without

reference to any particular coordinate system in that space . This measure will be

...

Page 576

PROOF . It

homeomorphism . To verify that it is an isomorphism , it will suffice to show that E

( q ) = 0 only when o is the void set $ . Now if E ( 0 ) = 0 , then X , = { 0 } and o ( T )

. = $ . It

PROOF . It

**follows**from Theorem 10 that the map o → E ( 0 ) is ahomeomorphism . To verify that it is an isomorphism , it will suffice to show that E

( q ) = 0 only when o is the void set $ . Now if E ( 0 ) = 0 , then X , = { 0 } and o ( T )

. = $ . It

**follows**...Page 689

The desired conclusion

a reflexive space , the averages A ( a ) are strongly convergent if they are

bounded and if T ( n ) / n converges to zero strongly . PROOF . This

The desired conclusion

**follows**from Corollary II.3.13 . Q.E.D. 3 COROLLARY . Ina reflexive space , the averages A ( a ) are strongly convergent if they are

bounded and if T ( n ) / n converges to zero strongly . PROOF . This

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

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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