## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 85

Page 1224

Nelson Dunford, Jacob T. Schwartz. ( b ) If T , is

extension T , of Tı , and , in particular , every self adjoint extension of Tı , satisfies

TCT , C7 * CT * . Proof . If T , CT , and ye D ( 7 % ) , then ( « , 7 * y ) = ( Tgx , y ) ( T

...

Nelson Dunford, Jacob T. Schwartz. ( b ) If T , is

**symmetric**then every**symmetric**extension T , of Tı , and , in particular , every self adjoint extension of Tı , satisfies

TCT , C7 * CT * . Proof . If T , CT , and ye D ( 7 % ) , then ( « , 7 * y ) = ( Tgx , y ) ( T

...

Page 1236

Every closed

( T * ) determined by a

, ... , k . Conversely , every such restriction T , of T * is a closed

Every closed

**symmetric**extension of T is the restriction of 1 * to the subspace of D( T * ) determined by a

**symmetric**family of boundary conditions , B. ( x ) = 0 , i = 1, ... , k . Conversely , every such restriction T , of T * is a closed

**symmetric**...Page 1272

Maximal

then it has proper

are different from zero . A maximal

proper ...

Maximal

**symmetric**operators . If T is a**symmetric**operator with dense domain ,then it has proper

**symmetric**extensions provided both of its deficiency indicesare different from zero . A maximal

**symmetric**operator is one which has noproper ...

### What people are saying - Write a review

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

### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

### 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 Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero