## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 81

Page 875

It will also be shown that this

preserving the operation of involution . This basic result , which is due to Gelfand

and Naïmark , will find many applications in the next two chapters . 3 LEMMA . 11

X is ...

It will also be shown that this

**isomorphism**is a * -**isomorphism**, i . e . , onepreserving the operation of involution . This basic result , which is due to Gelfand

and Naïmark , will find many applications in the next two chapters . 3 LEMMA . 11

X is ...

Page 878

There is one isometric * -

single out . In the notation of the preceding proof the * -

1 ( - ) ) of B * ( x ) onto Clo ( x ) ) has the property that x corresponds to the ...

There is one isometric * -

**isomorphism**of B * ( x ) onto C ( o ( x ) ) that we wish tosingle out . In the notation of the preceding proof the * -

**isomorphism**y H + y ( x -1 ( - ) ) of B * ( x ) onto Clo ( x ) ) has the property that x corresponds to the ...

Page 1373

of L2 ( 1 , { p is } ) into L2 ( 1 , { is } ) and an isometric

) into L ( 1 , { Âij } ) . Since { ais ( 2 ) } and { bij ( 2 ) } are inverse matrices , it

follows readily that AB = BA = 1 . Thus , A and B are isometric

all ...

of L2 ( 1 , { p is } ) into L2 ( 1 , { is } ) and an isometric

**isomorphism**of L ( 1 , { Mis }) into L ( 1 , { Âij } ) . Since { ais ( 2 ) } and { bij ( 2 ) } are inverse matrices , it

follows readily that AB = BA = 1 . Thus , A and B are isometric

**isomorphisms**ontoall ...

### What people are saying - Write a review

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

### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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