## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

### From inside the book

Results 1-3 of 81

Page 1064

But it is

But it is

**clear**that gm ( x ) + g ( x ) for all z . Hence q = g , proving that gl , $ 1,1 \ | \ , if f is in Co ( I ) and vanishes outside a bounded set . Next let | be in L , ( E " ) , and let { m } be a sequence of functions in ...Page 1652

Then , since | F 2 | F | , for each F in H ( * ) ( I ) , it is

Then , since | F 2 | F | , for each F in H ( * ) ( I ) , it is

**clear**that { Fn } converges to some F in Lề ( 1 ) . Similarly , since Fl ( ) 210F \ , for each F in H ( * ) ( I ) and each index J such that Jsk , it is**clear**that if J Sk ...Page 1725

Since the function qe defined by qe ( x ) = 9 ( ( 1- € ) x ) converges to q in the norm of CP ( I ) as ε = 0 by Lemma 2.5 , it is

Since the function qe defined by qe ( x ) = 9 ( ( 1- € ) x ) converges to q in the norm of CP ( I ) as ε = 0 by Lemma 2.5 , it is

**clear**that we may assume without loss of generality that q is in C % ( I ) . This will be assumed in what ...### 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 | |

37 other sections not shown

### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### 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 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