## Linear Operators, Part 2 |

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Page 1245

The Canonical Factorization In this section we shall prove that each closed

operator T with

where A is a positive ( i . e . , ( Ax , x ) > 0 , x e D ( A ) ) self adjoint transformation ...

The Canonical Factorization In this section we shall prove that each closed

operator T with

**dense**domain in Hilbert space has a unique factorization T = PA ,where A is a positive ( i . e . , ( Ax , x ) > 0 , x e D ( A ) ) self adjoint transformation ...

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 ) = \ Tx12 + \ x |

2 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 ) = \ Tx12 + \ x |

2 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 )

... 11 ( 21 )

the natural embedding of a B - space X into X * * in the X * topology , V . 4 .

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

**Dense**convex sets , V . 7 . 27 ( 437 )**Dense**... 11 ( 21 )

**density**of continuous functions in TM and L , , II1 ... 11 ( 21 )**Density**ofthe natural embedding of a B - space X into X * * in the X * topology , V . 4 .

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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