## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 1994

Let any

Theorem II . 3 . 6 proves ( 29 ) . ... F - 11n X , and since Ano

from the continuity of F that - Am ( 8 ) | 2 ds = 0 , m . no which implies ( III . 3 . 6 )

that in ...

Let any

**converge**for each o in H . Theorem 4 shows that lanl = nloo , andTheorem II . 3 . 6 proves ( 29 ) . ... F - 11n X , and since Ano

**converges**, we seefrom the continuity of F that - Am ( 8 ) | 2 ds = 0 , m . no which implies ( III . 3 . 6 )

that in ...

Page 2218

It must be shown that { Ex }

so a consideration of the sequence { Ea – E } shows that it may be assumed that

E = 0 . Thus , to make an indirect proof , it is assumed that the sequence { Ex } is ...

It must be shown that { Ex }

**converges**strongly to E . By Lemma 6 , E is in B andso a consideration of the sequence { Ea – E } shows that it may be assumed that

E = 0 . Thus , to make an indirect proof , it is assumed that the sequence { Ex } is ...

Page 2462

Moreover , if C belongs to the trace class C1 , then T , C

trace norm , and CT *

xe H | 1 } ) is conditionally compact , and thus for each € > 0 there exists a finite

set ...

Moreover , if C belongs to the trace class C1 , then T , C

**converges**to zero intrace norm , and CT *

**converges**to zero in trace norm . PROOF . The set K = C ( {xe H | 1 } ) is conditionally compact , and thus for each € > 0 there exists a finite

set ...

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