## Linear Operators: General theory |

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Page 183

it

Conversely , since $ ( EU EZ ) = $ ( EU ( E ) and $ ( E E2 ) = $ ( E4 ) ( E2 ) if E , E ,

belong to y , v ( uz , ° ( E ) ) is a nonnegative additive set function defined for E c ...

it

**follows**readily from the definition of v ( ug ) that v ( un , 6 - ( E ) ) 2 v ( U2 , E ) .Conversely , since $ ( EU EZ ) = $ ( EU ( E ) and $ ( E E2 ) = $ ( E4 ) ( E2 ) if E , E ,

belong to y , v ( uz , ° ( E ) ) is a nonnegative additive set function defined for E c ...

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 win 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 714

It

that I = Ep + Ep . Further T commutes with Ep and Ej so this direct sum

decomposition is into subspaces invariant under T . Statements ( a ) and ( b )

It

**follows**from its definition that Ep is a projection , that EPE ) = E , Ep = 0 , andthat I = Ep + Ep . Further T commutes with Ep and Ej so this direct sum

decomposition is into subspaces invariant under T . Statements ( a ) and ( b )

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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