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

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Page 2113

See also Apostol [ 4 , 5 , 11 , 15 ] , Colojoară and Foiaş [ 2 , 5 ] , Kariotis [ 1 ] , and

Vasilescu [ 3 , 4 , 5 , 6 , 7 , 8 ] for other results concerning decomposable

operators . Let H be a Hilbert space with an

See also Apostol [ 4 , 5 , 11 , 15 ] , Colojoară and Foiaş [ 2 , 5 ] , Kariotis [ 1 ] , and

Vasilescu [ 3 , 4 , 5 , 6 , 7 , 8 ] for other results concerning decomposable

operators . Let H be a Hilbert space with an

**orthonormal**basis { XnIn = 0 ...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

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 ) * . ( .Page 2453

Let H be a separable Hilbert space , and let T be a compact normal operator in H

. Let { wn } be a complete

Xn . Suppose that the sequence { \ n } contains no repetitions , and that all the ...

Let H be a separable Hilbert space , and let T be a compact normal operator in H

. Let { wn } be a complete

**orthonormal**set of eigenvectors of T , and let Txon = dnXn . Suppose that the sequence { \ n } contains no repetitions , and that all the ...

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