## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 78

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 * -

x ) ...

one * -

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

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

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

Page 1373

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

into L2 ( 4 , { Nis } ) . Since { aij ( 2 ) } and { bij ( 2 ) } are inverse matrices , it

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

all ...

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

**isomorphism**of L2 ( 1 ) , { Mis } )into L2 ( 4 , { Nis } ) . Since { aij ( 2 ) } and { bij ( 2 ) } are inverse matrices , it

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

**isomorphisms**ontoall ...

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero