## Linear Operators: Spectral theory |

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Results 1-3 of 87

Page 1020

( ais ) be the

1 , 0 , . . . , 0 ] , . . . , On = [ 0 , . . . , 0 , 1 ] . Let Ais denote the cofactor of the element

aij , i . e . , Aij is ( - 1 ) : + 3 times the determinant of the ( n - 1 ) × ( n - 1 )

( ais ) be the

**matrix**of an operator A in En relative to the orthonormal basis & z = [1 , 0 , . . . , 0 ] , . . . , On = [ 0 , . . . , 0 , 1 ] . Let Ais denote the cofactor of the element

aij , i . e . , Aij is ( - 1 ) : + 3 times the determinant of the ( n - 1 ) × ( n - 1 )

**matrix**...Page 1275

Jacobi

problem made in Section 8 can be carried ... An infinite

said to be a Jacobi

Jacobi

**Matrices**and the Moment Problem The investigations of the momentproblem made in Section 8 can be carried ... An infinite

**matrix**{ a ; k } , j , k 2 0 , issaid to be a Jacobi

**matrix**if ( i ) ( ii ) Apa = āap , Aipa = 0 , all p , q , 1p - 91 > 1 .Page 1338

Let { uis } be a positive

respect to a positive o - finite measure u . If the

defined by the equations Mijle ) = 5 . m . ; ( 2 ) u ( da ) , where e is any bounded

Borel ...

Let { uis } be a positive

**matrix**measure whose elements Mis are continuous withrespect to a positive o - finite measure u . If the

**matrix**of densities { mi ; } isdefined by the equations Mijle ) = 5 . m . ; ( 2 ) u ( da ) , where e is any bounded

Borel ...

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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