## Linear Operators: Spectral theory |

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Results 1-3 of 83

Page 1027

... the operator ET / ( T ) to the finite dimensional space EH . PROOF . ( a ) Since

H is infinite dimensional the origin

Suppose that 2 + 0

VII .

... the operator 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 , TheoremVII .

Page 1116

1 , B

plainly self adjoint and A

= p ( 1 - p / 2 ) - 1 . Thus , by Lemma 9 , T = BA

1 , B

**belongs**to the Hilbert - Schmidt class Cz . If we let Aqi = y1 = p2pi , then A isplainly self adjoint and A

**belongs**to the class Co , where r ( 1 - p / 2 ) = p , i . e . , r= p ( 1 - p / 2 ) - 1 . Thus , by Lemma 9 , T = BA

**belongs**to the class Cs , where s ...Page 1602

Then the point 2

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

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

but ...

Then the point 2

**belongs**to the essential spectrum of 1 ( Hartman and Wintner [14 ] ) . ( 48 ) Suppose that the function q is bounded below , and let | be a real

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

but ...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

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