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

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Page 1224

( b ) If T , is symmetric then every symmetric

( b ) If T , is symmetric then every symmetric

**extension**T , of T ,, and , in particular , every self adjoint**extension**of Tı , satisfies T , CT , CT CT * Proof . If T , CT , and y e D ( 1 * ) , then ( x , T * y ) = ( Tox , y ) ( T ...Page 1239

Conversely , let T , be a self adjoint

Conversely , let T , be a self adjoint

**extension**of T. Then by Lemma 26 , T is the restriction of T * to a subspace W of D ( T * ) determined by a symmetric family of linearly independent boundary conditions B1 ( x ) = 0 , i = 1 , ...Page 1270

**Extensions**of symmetric operators . The problem of determining whether a given symmetric operator has a self adjoint**extension**is of crucial importance in determining whether the spectral theorem may be employed .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### 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 |

### Common terms and phrases

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