## Linear Operators: Spectral theory |

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Page 876

Then ( y + Nie ) ( 2 ) = y ( 2 ) + Ni = i ( 1 + N ) , and

Then ( y + Nie ) ( 2 ) = y ( 2 ) + Ni = i ( 1 + N ) , and

**hence**1 + NI Sly + Niel .**Hence**( 1 + N ) 2 Sly + Niel2 = ( y + Nie ) ( y + Nie ) * 1 = | ( y + Nie ) ( y - Nie ) | y2 + Nael 1921 + N2 . Since this inequality must hold for all ...Page 1027

Suppose that 1 # 0 belongs to the spectrum of T. Since T is compact , Theorem VII.4.5 shows that 2 is an eigenvalue and

Suppose that 1 # 0 belongs to the spectrum of T. Since T is compact , Theorem VII.4.5 shows that 2 is an eigenvalue and

**hence**for some non - zero æ in H we have Tx = and**hence**, since T = TE , we have ( ET ) ( Ex ) 2 Ex .**Hence**a ...Page 1227

**Hence**T * x = ix , or x € Dr.**Hence**Dt is closed . Similarly , D_ is closed . Since D , and D are clearly linear subspaces of D ( T * ) , it remains to show that the spaces D ( T ) , D , and D are mutually orthogonal , and that their ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

Copyright | |

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