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

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Page 1953

First

x * in X * with x * # 0 and 2 * TX = 0 . Let x1 + 0 and define the operator A by the

equation Ax = x * ( x ) x1 , so that A + 0 . But AT = 0 , which contradicts Corollary ...

First

**suppose**that . = 0 . If TX is not dense then , by Corollary II . 3 . 13 , there is anx * in X * with x * # 0 and 2 * TX = 0 . Let x1 + 0 and define the operator A by the

equation Ax = x * ( x ) x1 , so that A + 0 . But AT = 0 , which contradicts Corollary ...

Page 2284

However , rather than seek the maximum generality , it will be convenient to

Both these properties hold for B if X is separable , so this will be assumed for the

rest of ...

However , rather than seek the maximum generality , it will be convenient to

**suppose**that B is itself complete and satisfies the countable chain condition .Both these properties hold for B if X is separable , so this will be assumed for the

rest of ...

Page 2303

enumeration of its spectrum . Let dn denote the distance from an to o ( T ) — { n } .

**Suppose**that E is its resolution of the identity , and**suppose**that { an } is anenumeration of its spectrum . Let dn denote the distance from an to o ( T ) — { n } .

**Suppose**that for all but a finite number of n , Elan ) has a onedimensional range .### What people are saying - Write a review

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