## Linear Operators: Spectral theory |

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Page 1120

Throughout the present section , we

Hilbert space is separable . Subdiagonal representations of an operator are

connected with the study of its invariant subspaces . Thus , the key to the situation

that we ...

Throughout the present section , we

**assume**for simplicity of statement thatHilbert space is separable . Subdiagonal representations of an operator are

connected with the study of its invariant subspaces . Thus , the key to the situation

that we ...

Page 1596

This assertion is not true if it is not

exercises in Section 9.D ) . Additional criteria are given below for the more

special operator 2 T = ( + g ( t ) dt . where the function q is

...

This assertion is not true if it is not

**assumed**that t is bounded below ( cf. theexercises in Section 9.D ) . Additional criteria are given below for the more

special operator 2 T = ( + g ( t ) dt . where the function q is

**assumed**to be real and...

Page 1611

We

differential operator of the form ( * ) on an interval which will be specified in each

case , and with the understanding that when no interval is mentioned , the result

is ...

We

**assume**, unless it is otherwise stated , that t is a formally symmetric formaldifferential operator of the form ( * ) on an interval which will be specified in each

case , and with the understanding that when no interval is mentioned , the result

is ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

### 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 Nauk 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