## Linear Operators: Spectral theory |

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Page 907

negative real axis respectively . Proof . If N is a bounded normal operator then ,

by Corollary IX . 3 . 15 , NN * = N * N = 1 if and only if Zī = 1 for every spectral ...

**positive**if and only if its spectrum lies on the unit circle , the real axis , or the non -negative real axis respectively . Proof . If N is a bounded normal operator then ,

by Corollary IX . 3 . 15 , NN * = N * N = 1 if and only if Zī = 1 for every spectral ...

Page 1247

... it follows that x = 0 . Q . E . D . Next we shall require some information on

adjoint transformation T is

, 00 ) ...

... it follows that x = 0 . Q . E . D . Next we shall require some information on

**positive**self adjoint transformations and their square roots . 2 LEMMA . A selfadjoint transformation T is

**positive**if and only if o ( T ) is a subset of the interval [ 0, 00 ) ...

Page 1338

Let { U is } be a

respect to a

by the equations Misle ) = m ( ) u ( da ) , where e is any bounded Borel set ...

Let { U is } 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 Misle ) = m ( ) u ( da ) , where e is any bounded Borel set ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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