## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 889

... since the spectrum of an operator is always closed ( IX.1.5 ) , every set in the

domain of a spectral measure satisfying ... a spectral measure which is defined

on the Boolean algebra B of all

for ...

... since the spectrum of an operator is always closed ( IX.1.5 ) , every set in the

domain of a spectral measure satisfying ... a spectral measure which is defined

on the Boolean algebra B of all

**Borel sets**in the plane and which satisfies ( iv )for ...

Page 894

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

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

regular operator valued set functions defined on the

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

Let E be the spectral resolution for T and let v,,(e) = (E(e)y,,, yn) for each

e. ... let {en} be a sequence of

if e is a Borel subset of the complement e; of en and 21:01 v,(e) = 0, then v,,(e) ...

Let E be the spectral resolution for T and let v,,(e) = (E(e)y,,, yn) for each

**Borel set**e. ... let {en} be a sequence of

**Borel sets**such that 22:01 v,(e,,) = 0, and such thatif e is a Borel subset of the complement e; of en and 21:01 v,(e) = 0, then v,,(e) ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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