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

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Page 2203

The mapping E HO ( E ) is clearly an isomorphism between B and the Boolean

algebra of all open and closed subsets of 1 . These open and closed sets o ( E )

form a

The mapping E HO ( E ) is clearly an isomorphism between B and the Boolean

algebra of all open and closed subsets of 1 . These open and closed sets o ( E )

form a

**basis**for the topology in 1 . To see this , note that sets of the form { a | | ( T ...Page 2313

None of this should cause the reader any essential difficulty . 9 LEMMA . Let E be

a projection of a B - space X onto a finite dimensional range and let E * : X * →X *

be its adjoint . Then , if 91 , 92 , . . . , On is a

None of this should cause the reader any essential difficulty . 9 LEMMA . Let E be

a projection of a B - space X onto a finite dimensional range and let E * : X * →X *

be its adjoint . Then , if 91 , 92 , . . . , On is a

**basis**for EX , we can find a unique ...Page 2451

RA | | 2 = | | A | | 2 n = 1 n = 1 Put ( 13 ) T ( A ) x = 3 ( im A * xn ) ( x , Qm ) xm n . m

= 1 In - dm nom for xe X and A € A . By Schwarz ' inequality , and since { xn } is an

orthonormal

RA | | 2 = | | A | | 2 n = 1 n = 1 Put ( 13 ) T ( A ) x = 3 ( im A * xn ) ( x , Qm ) xm n . m

= 1 In - dm nom for xe X and A € A . By Schwarz ' inequality , and since { xn } is an

orthonormal

**basis**, we have ( 14 ) ] ( 5 : 14 n = 1 m = 1 Im # n 16 . c ) * . ( .### What people are saying - Write a review

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