## Linear Operators, Part 2 |

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Page 1036

Then the infinite product h ; PA ( T ) = II ( 1 elila

analytic for 1 +0 . For each fixed a + 0 , 9 : ( T ) is a continuous complex valued

function on the B - space of all Hilbert - Schmidt operators . Proof . First note that if

...

Then the infinite product h ; PA ( T ) = II ( 1 elila

**converges**and defines a functionanalytic for 1 +0 . For each fixed a + 0 , 9 : ( T ) is a continuous complex valued

function on the B - space of all Hilbert - Schmidt operators . Proof . First note that if

...

Page 1333

Since gn +0 and TR ( 2 ; T ) is a bounded operator , it follows that R ( 2 ; T ) gn

and TR ( 2 ; T ) g ,

,9 : 14 ;

.

Since gn +0 and TR ( 2 ; T ) is a bounded operator , it follows that R ( 2 ; T ) gn

and TR ( 2 ; T ) g ,

**converge**to zero in L ( 1 ) . Thus by Lemma 2.16 the series , ( 7,9 : 14 ;

**converges**to f in the topology of C " - ' ( J ) for each compact interval J of 1.

Page 1436

Let { en } be a bounded sequence of elements of D ( T ) such that { Tin }

each j , 1 si Sk . Then ħ ; = h ; - & t = 1 * ( hi ) p , is in D , and Thi . Thus { ñ ; }

Let { en } be a bounded sequence of elements of D ( T ) such that { Tin }

**converges**. Find a subsequence { 8n ; } = { h ; } such that x * ( hi )**converges**foreach j , 1 si Sk . Then ħ ; = h ; - & t = 1 * ( hi ) p , is in D , and Thi . Thus { ñ ; }

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

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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