## Linear Operators, Part 2 |

### From inside the book

Results 1-3 of 79

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 . If

X is a ...

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 . If

X is a ...

Page 878

one * -

isometric * -

the notation of the preceding proof the * -

...

one * -

**isomorphism**of B * ( x ) onto C ( o ( x ) ) into another one . There is oneisometric * -

**isomorphism**of B * ( x ) onto C ( g ( x ) ) that we wish to single out . Inthe notation of the preceding proof the * -

**isomorphism**y H y ( x - 1 ( • ) ) of B * ( x )...

Page 1355

_ Lz ( u , e ; ) ) that V is an isometric

} ) and that A is an isometric

Lalu , de ; ) of L2 ( u , e ; ) . To prove ( ii ) , note that since G vanishes outside of 1

...

_ Lz ( u , e ; ) ) that V is an isometric

**isomorphism**of E ( 1 ) LZ ( I ) onto L ( 1 , { pis} ) and that A is an isometric

**isomorphism**of L2 ( 1 , { pis } ) onto the subspace –Lalu , de ; ) of L2 ( u , e ; ) . To prove ( ii ) , note that since G vanishes outside of 1

...

### 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 | |

57 other sections not shown

### Other editions - View all

### Common terms and phrases

additive adjoint operator 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 derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function give 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