## Linear Operators, Part 2 |

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Page 889

This means that for every sequence { 8 ; } of disjoint

8 ; ) x , ) XEH . i = 1 i = 1 A spectral measure E defined on the

plane and satisfying ( iv ) for every

of ...

This means that for every sequence { 8 ; } of disjoint

**Borel sets**( v ) Σ Ε ( δ , ) E ( U8 ; ) x , ) XEH . i = 1 i = 1 A spectral measure E defined on the

**Borel sets**in theplane and satisfying ( iv ) for every

**Borel set**d and ( v ) for every sequence { 8 ; }of ...

Page 894

6.2 ) that x * E ( 8 ) x O for every

* € X * . It follows ( II.3.15 ) that E ( S ) = 0 . Thus if E and A are bounded additive

regular operator valued set functions defined on the

6.2 ) that x * E ( 8 ) x O for every

**Borel set**8 in S and every pair x , ** with x e X , x* € X * . It follows ( II.3.15 ) that E ( S ) = 0 . Thus if E and A are bounded additive

regular operator valued set functions defined on the

**Borel sets**of a normal ...Page 913

... basis for H , whose initial element is yo . Let E be the spectral resolution for T

and let vn ( e ) = ( E ( e ) yn , yn ) for each

decomposition theorem ( III.4.14 ) , let { en } be a sequence of

...

... basis for H , whose initial element is yo . Let E be the spectral resolution for T

and let vn ( e ) = ( E ( e ) yn , yn ) for each

**Borel set**e . Using the Lebesguedecomposition theorem ( III.4.14 ) , let { en } be a sequence of

**Borel sets**such that...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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