## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 79

Page 876

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

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

**hence**1 + N < ly + Niel .**Hence**N ( 1 + N ) 2 = \ y + Nie | 2 = | ( y + Nie ) ( y + Nie ) * 1 = | ( y + Nie ) ( y - Nie ) \ y2 + Nel = 1741 + N2 . Since this inequality must hold ...Page 1027

**Hence**a belongs to the spectrum of ET . Conversely , suppose that a non - zero scalar , belongs to the spectrum of ET . Then , for some non - zero x in EH , we have ETx = 2x . Then Tx = 2x + y , where y belongs to the , subspace ( I - E ) ...Page 1227

**Hence**T * x = ir , or xe Dr.**Hence**D. is closed . Similarly , = Dt D is closed . Since D4 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 ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

13 other sections not shown

### Other editions - View all

### Common terms and phrases

additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero