## Linear Operators: Spectral theory |

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Page 1239

Conversely, let T be a self adjoint

restriction of To to a subspace Q3 of Q(T*) determined by a symmetric family of

linearly independent boundary conditions B, (a) = 0, i = 1,..., k, and we have only

to ...

Conversely, let T be a self adjoint

**extension**of T. Then by Lemma 26, T, is therestriction of To to a subspace Q3 of Q(T*) determined by a symmetric family of

linearly independent boundary conditions B, (a) = 0, i = 1,..., k, and we have only

to ...

Page 1261

23 If an operator T has a closed linear

linear

is called the closure of T. (a) There exists a densely defined operator with no

closed ...

23 If an operator T has a closed linear

**extension**there exists a unique closedlinear

**extension**T such that if T is any closed linear**extension**of T then TC T1, Tis called the closure of T. (a) There exists a densely defined operator with no

closed ...

Page 1270

The problem of determining whether a given symmetric operator has a self

adjoint

affirmative, it is important to know what the self adjoint

how they ...

The problem of determining whether a given symmetric operator has a self

adjoint

**extension**is of crucial importance in ... If the answer to this problem isaffirmative, it is important to know what the self adjoint

**extensions**look like andhow they ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 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 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