## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 77

Page 1027

Hence a

scalar 1

have ETx = 2x . Then Tx = 2x + y , where y

...

Hence a

**belongs**to the spectrum of ET . Conversely , suppose that a non - zeroscalar 1

**belongs**to the spectrum of ET . Then , for some non - zero x in EH , wehave ETx = 2x . Then Tx = 2x + y , where y

**belongs**to the subspace ( I - EH , and...

Page 1116

1 , B

plainly self adjoint and A

= p ( 1 - p / 2 ) - 1 . Thus , by Lemma 9 , T = BA

1 , B

**belongs**to the Hilbert - Schmidt class Cz . If we let Aq ; = r ? - plaqi , then A isplainly self adjoint and A

**belongs**to the class Co , where r ( 1 - p / 2 ) = p , i . e . , r= p ( 1 - p / 2 ) - 1 . Thus , by Lemma 9 , T = BA

**belongs**to the class Cs , where ...Page 1602

Then the point 2

14 ] ) . ( 48 ) Suppose that the function q is bounded below , and let | be a real

solution of the equation ( 2 - 1 ) } = 0 on [ 0 , 00 ) which is not square - integrable

but ...

Then the point 2

**belongs**to the essential spectrum of 7 ( Hartman and Wintner [14 ] ) . ( 48 ) Suppose that the function q is bounded below , and let | be a real

solution of the equation ( 2 - 1 ) } = 0 on [ 0 , 00 ) which is not square - integrable

but ...

### What people are saying - Write a review

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

### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

37 other sections not shown

### Other editions - View all

### Common terms and phrases

additive 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 differential equations 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 neighborhood norm obtained partial positive preceding present problem Proc 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