## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 84

Page 1187

Just as in the case of a

is defined to be the set of all complex numbers a such that ( 21 - T ) -1 exists as

an everywhere defined

Just as in the case of a

**bounded operator**the resolvent set p ( T ) of an operator Tis defined to be the set of all complex numbers a such that ( 21 - T ) -1 exists as

an everywhere defined

**bounded operator**. For å in p ( T ) the symbol R ( 2 ; T ) ...Page 1190

It is said to be self adjoint if T = 1 * . An

having a dense domain but if D ( T ) is dense so that T * is defined then the notion

of symmetry is equivalent to the inclusion T * 2 T. Of course if T is a

It is said to be self adjoint if T = 1 * . An

**operator**T may be symmetric withouthaving a dense domain but if D ( T ) is dense so that T * is defined then the notion

of symmetry is equivalent to the inclusion T * 2 T. Of course if T is a

**bounded**...Page 1273

Weyl [ 5 ] showed this to be the case for differential

that the inverse

set y ...

Weyl [ 5 ] showed this to be the case for differential

**operators**. If T is a linear**operator**with dense domain , let y ( T ) be the set of all complex numbers à suchthat the inverse

**operator**( T - 21 ) -1 exists and is**bounded**on its domain . Theset y ...

### 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 | |

57 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 complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined 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 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