## Linear Operators: Spectral theory |

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Page 1079

Nelson Dunford, Jacob T. Schwartz. making Em into a Hilbert space . If A is a

matrix as in

equation ( A ( m ) b ) ( i7 , . . . , im ) = { ainda . . . dimom b ( j1 , . . . , im ) . 1 , . . , İm

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Nelson Dunford, Jacob T. Schwartz. making Em into a Hilbert space . If A is a

matrix as in

**Exercise**25 , let A ( m ) be the transformation in Em defined by theequation ( A ( m ) b ) ( i7 , . . . , im ) = { ainda . . . dimom b ( j1 , . . . , im ) . 1 , . . , İm

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Page 1083

Consequently , the series 00 4 ( 2 ) — 28 ( 1 ) 1 = £4 , 25 N = 2 of the preceding

measure space . Then an operator A in the Hilbert space L2 ( S , E , u ) is of ...

Consequently , the series 00 4 ( 2 ) — 28 ( 1 ) 1 = £4 , 25 N = 2 of the preceding

**exercise**converges in the Hilbert - Schmidt norm . 44 Let ( S , E , u ) be a positivemeasure space . Then an operator A in the Hilbert space L2 ( S , E , u ) is of ...

Page 1086

Show , finally , that by choosing A ( s , 3 ) = 0 for all s in S , we obtain the result of

method of

of ...

Show , finally , that by choosing A ( s , 3 ) = 0 for all s in S , we obtain the result of

**Exercise**46 as a special case of the present result . ( Hint : Generalize themethod of

**Exercise**46 . ) 49 The operator A of Hilbert - Schmidt class is said to beof ...

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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