## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 90

Page 1246

We may also regard A as a mapping from the

the space Hı . In this case A is still continuous , for | Axli = ( Ax , Ax ) , = ( A x , x ) ,

= ( Ax , x ) , xe D ( T ) , and , by the inequalities above , ( Ax , x ) = | AX | \ x ...

We may also regard A as a mapping from the

**dense**subspace D ( T ) of H intothe space Hı . In this case A is still continuous , for | Axli = ( Ax , Ax ) , = ( A x , x ) ,

= ( Ax , x ) , xe D ( T ) , and , by the inequalities above , ( Ax , x ) = | AX | \ x ...

Page 1271

Let T be a symmetric operator with domain D ( T )

) , we have | ( T£il ) x12 = ( Tx , Tx ) Fi ( x , Tx ) + i ( Tx , x ) + ( x , x ) = | Tx12 + \ x |

2 2 \ Q12 . This shows that if ( T£il ) x = 0 , then x = 0 and so the operators T il ...

Let T be a symmetric operator with domain D ( T )

**dense**in H . Then if x is in D ( T) , we have | ( T£il ) x12 = ( Tx , Tx ) Fi ( x , Tx ) + i ( Tx , x ) + ( x , x ) = | Tx12 + \ x |

2 2 \ Q12 . This shows that if ( T£il ) x = 0 , then x = 0 and so the operators T il ...

Page 1905

14 ( 132 ) Saks decomposition , IV . 9 . 7 ( 308 ) Yosida - Hewitt decomposition , (

233 ) Deficiency indices and spaces , definition , XII . 4 . 9 ( 1226 ) De Morgan ,

rules of , ( 2 )

14 ( 132 ) Saks decomposition , IV . 9 . 7 ( 308 ) Yosida - Hewitt decomposition , (

233 ) Deficiency indices and spaces , definition , XII . 4 . 9 ( 1226 ) De Morgan ,

rules of , ( 2 )

**Dense**convex sets , V . 7 . 27 ( 437 )**Dense**linear manifolds , V . 7 .### 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