## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 84

Page 1015

If lim Tn = T in the

of the integral in [ * ] contains o ( Tn ) for all sufficiently large n . From Corollary VII

. 6 . 3 it is seen that , in the

...

If lim Tn = T in the

**norm**of HS it follows from Lemma VII . 6 . 5 that the contour Cof the integral in [ * ] contains o ( Tn ) for all sufficiently large n . From Corollary VII

. 6 . 3 it is seen that , in the

**norm**of HS + , | lim [ A , - 1 , 3 - 1 = [ A , – T ] - 1 th - > 0...

Page 1297

The first

. Now Ti ( t ) is an adjoint ( Theorem 10 ) ; therefore ( cf . XII . 1 . 6 ) D ( T1 ( T ) ) is

complete in the

The first

**norm**is the**norm**of the pair [ 1 , T , / ] as an element of the graph of T ( T ). Now Ti ( t ) is an adjoint ( Theorem 10 ) ; therefore ( cf . XII . 1 . 6 ) D ( T1 ( T ) ) is

complete in the

**norm**fli . Since the two additional terms in \ | \ 2 are the**norm**of ...Page 1431

( e ) The closure of D ( T . ( t ' ) ) in the

closure of D ( T . ( t ' ) ) in the

D ( T . ( t ' ) ) in the

) we ...

( e ) The closure of D ( T . ( t ' ) ) in the

**norm**of D ( T ( ' ) ) coincides with theclosure of D ( T . ( t ' ) ) in the

**norm**of D ( T ( ) ) . Let D , and D , be the closures ofD ( T . ( t ' ) ) in the

**norms**of D ( T2 ( t ' ) ) and D ( T1 ( T ) ) respectively . By step ( c) we ...

### What people are saying - Write a review

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

### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 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 adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero