## Linear Operators, Part 2 |

### From inside the book

Results 1-3 of 78

Page 898

If we put E ( 8 ) = 0 ) when d n o ( T ) is void , then

from Theorem 1 and

defined spectral measure associated , in

is ...

If we put E ( 8 ) = 0 ) when d n o ( T ) is void , then

**Corollary**4 follows immediatelyfrom Theorem 1 and

**Corollary**IX.3.15 . Q.E.D. 5 DEFINITION . The uniquelydefined spectral measure associated , in

**Corollary**4 , with the normal operator Tis ...

Page 1142

We note the following

bounded map of C , into Cp , 1 < p < . ( b ) If H is anti - Hermitian , then the anti -

Hermitian part of tH is nH . ( c ) tH leaves invariant the range of each of the

projections E ...

We note the following

**corollary**. 13**COROLLARY**. ( a ) The mapping t is abounded map of C , into Cp , 1 < p < . ( b ) If H is anti - Hermitian , then the anti -

Hermitian part of tH is nH . ( c ) tH leaves invariant the range of each of the

projections E ...

Page 1301

However , as vo satisfies an equation of order 2n , v , must be identically zero .

This contradiction completes the proof . Q.E.D. 23

formal differential operator of order n on an interval I with end points a , b , and

suppose ...

However , as vo satisfies an equation of order 2n , v , must be identically zero .

This contradiction completes the proof . Q.E.D. 23

**COROLLARY**. Let T be aformal differential operator of order n on an interval I with end points a , b , and

suppose ...

### 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 | |

11 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 function f 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 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