## Linear Operators: Spectral theory |

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Page 906

1 DEFINITION . A bounded operator T in Hilbert space H is called unitary if TT * =

T * T = 1 ; it is called self adjoint , symmetric or Hermitian if T = T * ;

self adjoint and if ( Tx , x ) 20 for every x in H ; and

1 DEFINITION . A bounded operator T in Hilbert space H is called unitary if TT * =

T * T = 1 ; it is called self adjoint , symmetric or Hermitian if T = T * ;

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

**positive**definite if it is**positive**...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 { M is } be a

respect to a

defined by the equations Mijle ) = S. m.:(2)u(da ) , where e is any bounded Borel

set ...

Let { M is } be a

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

**positive**o - finite measure u . If the matrix of densities { mis } isdefined by the equations Mijle ) = S. m.:(2)u(da ) , where e is any bounded Borel

set ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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