## Linear Operators, Part 2 |

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Page 1224

( b ) If T , is symmetric then every symmetric

every self adjoint

ye D ( T * ) , then ( x , 7 * y ) = ( T2x , y ) = ( 1 x , y ) for any xED ( T ) . Hence y eD ...

( b ) If T , is symmetric then every symmetric

**extension**T , of Tj and , in particular ,every self adjoint

**extension**of Tı , satisfies T , CT , C7 * CT * Proof . If T , CT , andye D ( T * ) , then ( x , 7 * y ) = ( T2x , y ) = ( 1 x , y ) for any xED ( T ) . Hence y eD ...

Page 1239

Conversely , let T , be a self adjoint

restriction of T * to a subspace W of D ( T * ) determined by a symmetric family of

linearly independent boundary conditions B ; ( x ) = 0 , i = 1 , . . . , k , and we ...

Conversely , let T , be a self adjoint

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

linearly independent boundary conditions B ; ( x ) = 0 , i = 1 , . . . , k , and we ...

Page 1270

symmetric operator has a self adjoint

determining whether the spectral theorem may be employed . If the answer to this

...

**Extensions**of symmetric operators . The problem of determining whether a givensymmetric operator has a self adjoint

**extension**is of crucial importance indetermining whether the spectral theorem may be employed . If the answer to this

...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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