## Linear Operators: Spectral theory |

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Page 1027

... ET / ( T ) to the finite dimensional space EH . PROOF . ( a ) Since H is infinite

dimensional the origin

# 0

... ET / ( T ) to the finite dimensional space EH . PROOF . ( a ) Since H is infinite

dimensional the origin

**belongs**to the spectrum of both T and ET . Suppose that 2# 0

**belongs**to the spectrum of T. Since T is compact , Theorem VII.4.5 shows ...Page 1116

Then plainly Σ | Βφ.12 = Σ ( 1852 < α , so that , by Definition 6.1 , B

Hilbert - Schmidt class Cz . If we let Aqi = y1 = p20i , then A is plainly self adjoint

and A

Then plainly Σ | Βφ.12 = Σ ( 1852 < α , so that , by Definition 6.1 , B

**belongs**to theHilbert - Schmidt class Cz . If we let Aqi = y1 = p20i , then A is plainly self adjoint

and A

**belongs**to the class C ,, where r ( 1 - p / 2 ) = p , i.e. , r = p ( 1 - p / 2 ) -1 .Page 1602

Then the point à

14 ] ) . ( 48 ) Suppose that the function q is bounded below , and let i be a real

solution of the equation ( 2-1 ) } = 0 on [ 0 , 0 ) which is not square - integrable but

...

Then the point à

**belongs**to the essential spectrum of T ( Hartman and Wintner [14 ] ) . ( 48 ) Suppose that the function q is bounded below , and let i be a real

solution of the equation ( 2-1 ) } = 0 on [ 0 , 0 ) which is not square - integrable but

...

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