## Linear Operators: Spectral theory |

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Page 1036

Then the infinite product qa ( T ) = ( 1 ( 1-1 ) elila

function analytic for 1 # 0 . For each fixed 1 # 0 , P. ( T ) is a continuous complex

valued function on the B - space of all Hilbert - Schmidt operators . PROOF . First

note ...

Then the infinite product qa ( T ) = ( 1 ( 1-1 ) elila

**converges**and defines afunction analytic for 1 # 0 . For each fixed 1 # 0 , P. ( T ) is a continuous complex

valued function on the B - space of all Hilbert - Schmidt operators . PROOF . First

note ...

Page 1420

Then , by assumption ( b ) , { In }

' ) ) . Conversely , let { fr }

, let Ital + \ T2 ( t + t ' ) [ nl → 0 . If { { n } is not bounded in D ( TZ ( T ) ) , there is a ...

Then , by assumption ( b ) , { In }

**converges**to zero in the topology of D ( T / ( 1 + r' ) ) . Conversely , let { fr }

**converge**to zero in the topology of D ( T1 ( + ' ) ) , that is, let Ital + \ T2 ( t + t ' ) [ nl → 0 . If { { n } is not bounded in D ( TZ ( T ) ) , there is a ...

Page 1436

Let { gn } be a bounded sequence of elements of D ( T ) such that { Tg , }

each j , 1 sisk . Then hi ' = h : - * _ * ( ha ) q ; is in D , and Tħ = Thị . Thus { ñ ; }

Let { gn } be a bounded sequence of elements of D ( T ) such that { Tg , }

**converges**. Find a subsequence { 8n ; } { h ; } such that w * ( hi )**converges**foreach j , 1 sisk . Then hi ' = h : - * _ * ( ha ) q ; is in D , and Tħ = Thị . Thus { ñ ; }

**converges**...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

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