## Linear Operators: Spectral theory |

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Page 1188

If the domain D ( T ) of the operator T is

consists , by definition , of all y in H for which ( Tx , y ) is continuous for x in D ( T )

. Since D ( T ) is

H ...

If the domain D ( T ) of the operator T is

**dense**in H then the domain D ( T * )consists , by definition , of all y in H for which ( Tx , y ) is continuous for x in D ( T )

. Since D ( T ) is

**dense**in v there is ( IV . 4 . 5 ) a uniquely determined point y * inH ...

Page 1271

Let T be a symmetric operator with domain D ( T )

) , we have | ( T£il ) x | 2 = ( Tx , Tx ) Fi ( x , Tx ) £i ( Tx , x ) + ( x , x ) = | Tx | 2 + 1

2012 2 \ x12 . This shows that if ( T£il ) x = 0 , then x = 0 and so the operators T il ...

Let T be a symmetric operator with domain D ( T )

**dense**in H . Then if x is in D ( T) , we have | ( T£il ) x | 2 = ( Tx , Tx ) Fi ( x , Tx ) £i ( Tx , x ) + ( x , x ) = | Tx | 2 + 1

2012 2 \ x12 . This shows that if ( T£il ) x = 0 , then x = 0 and so the operators T il ...

Page 1905

9 ( 1226 ) De Morgan , rules of , ( 2 )

298 )

. 4 .

9 ( 1226 ) De Morgan , rules of , ( 2 )

**Dense**convex sets , V . 7 . 27 ( 437 ) ... 19 (298 )

**density**of simple functions in Lp , isp < 00 , III . 3 . 8 ( 125 ) ... 11 ( 21 )**Density**of the natural embedding of a B - space X into X * * in the & * topology , V. 4 .

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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