## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 73

Page 1188

Similarly whenever the inverse T - 1 is mentioned it is tacitly

one - to - one . We recall that the orthocomplement of a set U in H is defined as

the set { x \ x e H , ( x , A ) = 0 } . This orthocomplement is denoted by HOA or by

A4 .

Similarly whenever the inverse T - 1 is mentioned it is tacitly

**assumed**that T isone - to - one . We recall that the orthocomplement of a set U in H is defined as

the set { x \ x e H , ( x , A ) = 0 } . This orthocomplement is denoted by HOA or by

A4 .

Page 1724

be plane . This being

follows . The general process of reducing the proof to the special case in which

the ...

**Assuming**the boundary to be smooth , it follows that it may as well be**assumed**tobe plane . This being

**assumed**, the proof of Theorem 2 may be modified asfollows . The general process of reducing the proof to the special case in which

the ...

Page 1734

This will be

the mapping Q , and of Lemmas 3 . 47 and 3 . 48 , we see that we may assume

without loss of generality that 1 . = V , I = V / , and q = 0 . All this will also be ...

This will be

**assumed**in what follows . Making use of the properties ( i ) and ( ii ) ofthe mapping Q , and of Lemmas 3 . 47 and 3 . 48 , we see that we may assume

without loss of generality that 1 . = V , I = V / , and q = 0 . All this will also be ...

### 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

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint operator 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