## Linear Operators: Spectral theory |

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Page 906

... self adjoint , symmetric or Hermitian if T = T * ;

Tx , x ) 20 for every x in H ; and

every x + 0 in H . It is clear that all of these classes of operators are normal .

... self adjoint , symmetric or Hermitian if T = T * ;

**positive**if it is self adjoint and if (Tx , x ) 20 for every x in H ; and

**positive**definite if it is**positive**and ( Tx , x ) > 0 forevery 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

transformations and their square roots . 2 LEMMA . A self adjoint transformation T

is

the ...

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

**positive**self adjointtransformations 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 . Let E bethe ...

Page 1338

Let { uis } be a

respect to a

by the equations Mile ) = 5 . m ; ( 2 ) u ( da ) , where e is any bounded Borel set ...

Let { uis } be a

**positive**matrix measure whose elements Mis are continuous withrespect to a

**positive**o - finite measure u . If the matrix of densities { mij } is definedby the equations Mile ) = 5 . m ; ( 2 ) u ( da ) , where e is any bounded Borel set ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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