## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 69

Page 1258

Conversely , any such maximal symmetric operator is the infinitesimal generator

of a strongly continuous semi - group of partially

domain H . Hilbert space H may be decomposed into an orthogonal direct sum H

...

Conversely , any such maximal symmetric operator is the infinitesimal generator

of a strongly continuous semi - group of partially

**isometric**operators with initialdomain H . Hilbert space H may be decomposed into an orthogonal direct sum H

...

Page 1272

9 , and that an

, if dd = 0 ) = d _ . Also it is clear that a closed

extension if and only if there is an

...

9 , and that an

**isometric**operator V is unitary if and only if D ( V ) H = R ( V ) , i . e ., if dd = 0 ) = d _ . Also it is clear that a closed

**isometric**operator has a unitaryextension if and only if there is an

**isometric**mapping of Dt onto D _ , and that this...

Page 1373

of L ( 1 , { Pi } ) into L2 ( 1 , { i } ) and an

into L2 ( 1 , Ais } ) . Since { ajj ( a ) } and { bis ( a ) } are inverse matrices , it follows

readily that AB = BA = I . Thus , A and B are

of L ( 1 , { Pi } ) into L2 ( 1 , { i } ) and an

**isometric**isomorphism of L , ( 4 , { Wix } )into L2 ( 1 , Ais } ) . Since { ajj ( a ) } and { bis ( a ) } are inverse matrices , it follows

readily that AB = BA = I . Thus , A and B are

**isometric**isomorphisms onto all of ...### 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 | |

36 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 singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero