## Linear Operators: Spectral theory |

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Page 1224

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. ( b ) If T ,

is

self adjoint extension of Tı , satisfies T , CT , CT CT * Proof . If T , CT , and ye D ( T

...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. ( b ) If T ,

is

**symmetric**then every**symmetric**extension T , of Tı , and , in particular , everyself adjoint extension of Tı , satisfies T , CT , CT CT * Proof . If T , CT , and ye D ( T

...

Page 1236

Every closed

( T * ) determined by a

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

Every closed

**symmetric**extension of T is the restriction of T * to the subspace of D( T * ) determined by a

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

**symmetric**...Page 1272

123 ] and Ahiezer and Glazman [ 1 ; Secs . 78 – 80 ] . Maximal

operators . If T is a

zero .

123 ] and Ahiezer and Glazman [ 1 ; Secs . 78 – 80 ] . Maximal

**symmetric**operators . If T is a

**symmetric**operator with dense domain , then it has proper**symmetric**extensions provided both of its deficiency indices are different fromzero .

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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