## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 87

Page 1378

Suppose that 01 , . . . , 07 is a determining set for T . Then it is evident from

, k , Pijle ) = 0 if i > k or j > k , we get a matrix measure { Pis } which by Corollary

21 ...

Suppose that 01 , . . . , 07 is a determining set for T . Then it is evident from

**Theorem**23 that if we define { pish , i , j = 1 , . . . , n , by Pijle ) = Pijle ) , i , j = 1 , . . ., k , Pijle ) = 0 if i > k or j > k , we get a matrix measure { Pis } which by Corollary

21 ...

Page 1379

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. { ź is } is

the matrix measure of

each e C N . Since 1 is the union of a sequence of neighborhoods of the same ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. { ź is } is

the matrix measure of

**Theorem**23 , the values Pile ) are uniquely determined foreach e C N . Since 1 is the union of a sequence of neighborhoods of the same ...

Page 1904

15 remarks on , ( 389 - 392 ) Convergence

continuous limits , IV . 6 . 11 ( 268 ) Banach

measurable ...

15 remarks on , ( 389 - 392 ) Convergence

**theorems**, . IV . 15 Alexandroff**theorem**on convergence of measures , IV . 9 . 15 ( 316 ) Arzelą**theorem**oncontinuous limits , IV . 6 . 11 ( 268 ) Banach

**theorem**for operators into space ofmeasurable ...

### What people are saying - Write a review

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

### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 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 shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero