## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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**positive**if it is self adjoint and if ( Tx , x ) 20 for every x in H ; and**positive**definite if it is**positive**and ( Tr , x ) > 0 for every x + 0 in H. It is clear that all of these classes of operators are normal .Page 1247

Q.E.D. Next we shall require some information on

Q.E.D. Next we shall require some information on

**positive**self adjoint transformations and their square roots . 2 LEMMA . A self adjoint transformation T is**positive**if and only if o ( T ) is a subset of the interval [ 0 , 0 ) . PROOF .Page 1338

Let { uis } be a

Let { uis } be a

**positive**matrix measure whose elements Mis are continuous with respect to a**positive**o - finite measure u . If the matrix of densities { mij } is defined by the equations Mijle ) = S.m. , ( 2 ) u ( da ) , where e is any ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

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