## Linear Operators, Part 2 |

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Page 1224

( b ) If T , is

every self adjoint extension of Tı , satisfies T , CT , C7 * CT * Proof . If T , CT , and

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 , and

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

Page 1236

Every closed

D ( T * ) determined by a

1 , . . . , k . Conversely , every such restriction T , of T * is a closed

Every closed

**symmetric**extension of T is the restriction of T ' * to the subspace ofD ( T * ) determined by a

**symmetric**family of boundary conditions , B ; ( x ) = 0 , i =1 , . . . , k . Conversely , every such restriction T , of T * is a closed

**symmetric**...Page 1272

Maximal

then it has proper

are different from zero . A maximal

proper ...

Maximal

**symmetric**operators . If T is a**symmetric**operator with dense domain ,then it has proper

**symmetric**extensions provided both of its deficiency indicesare different from zero . A maximal

**symmetric**operator is one which has noproper ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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