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

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Page 2215

Thus the conclusion

LEMMA . Let B be a bounded o - complete Boolean algebra of projections in a B -

space X . Suppose that , for some sequence { x ; } in X , X = sp { Ex : | E e B , i 2 1

} .

Thus the conclusion

**follows from Lemma**14 and Corollary 15 . Q . E . D . 21LEMMA . Let B be a bounded o - complete Boolean algebra of projections in a B -

space X . Suppose that , for some sequence { x ; } in X , X = sp { Ex : | E e B , i 2 1

} .

Page 2308

10 and by

remark preceding Definition XIII . 2 . 29 , that S is closed . From this , it

immediately that S - XI is closed , and hence from

- 1 is ...

10 and by

**Lemma**XII . 1 . 6 ( a ) , it**follows**from Definition XIII . 2 . 17 and theremark preceding Definition XIII . 2 . 29 , that S is closed . From this , it

**follows**immediately that S - XI is closed , and hence from

**Lemma**XII . 1 . 5 , that ( 8 – 17 )- 1 is ...

Page 2364

Since R ( do ; T ) is compact by Lemma 2 . 2 , it

Theorem VI . 5 . 4 that K ( n ) is a compact operator which depends analytically on

n for ini < + 84 . It

Since R ( do ; T ) is compact by Lemma 2 . 2 , it

**follows from Lemma**VII . 6 . 6 andTheorem VI . 5 . 4 that K ( n ) is a compact operator which depends analytically on

n for ini < + 84 . It

**follows from Lemma**VII . 6 . 6 that if O is any bounded open ...### What people are saying - Write a review

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