## 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 | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero