## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 88

Page 984

The set of functions f in L ( R ) for which f vanishes in a neighborhood of infinity is

The set of functions f in L ( R ) for which f vanishes in a neighborhood of infinity is

**dense**in Ly ( R ) . Proof . It follows from Lemma 3.6 that the set of all functions in L2 ( R , B , u ) which vanish outside of compact sets is ...Page 1245

The Canonical Factorization In this section we shall prove that each closed operator T with

The Canonical Factorization In this section we shall prove that each closed operator T with

**dense**domain in Hilbert space has a unique factorization T = PA , where A is a positive ( i.e. , ( Ax , x ) > 0 , x € D ( A ) ) self adjoint ...Page 1246

We may also regard A as a mapping from the

We may also regard A as a mapping from the

**dense**subspace D ( T ) of H into the space Hz . In this case A is still continuous , for | Axlî = ( Ax , Ax ) , = ( Ao x , x ) , = ( Ax , x ) , e ( T ) , and , by the inequalities above ...### What people are saying - Write a review

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

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

46 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 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero