## Linear Operators: Spectral theory |

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Page 1162

... one correspondence with the points of Mo , i . e . , with all the maximal ideals of

the algebra

of M . Now in an algebra with identity every ideal is contained in a maximal ideal

...

... one correspondence with the points of Mo , i . e . , with all the maximal ideals of

the algebra

**obtained**by adjoining an identity to L ( R ) except the point at infinityof M . Now in an algebra with identity every ideal is contained in a maximal ideal

...

Page 1318

Suppose that the homogeneous system

has a non - trivial solution & ( c ) , B7 ( c ) , and let K . ( - ) be the function ( of the

variable s )

...

Suppose that the homogeneous system

**obtained**from equations [ l ' ] and [ 2 ' ]has a non - trivial solution & ( c ) , B7 ( c ) , and let K . ( - ) be the function ( of the

variable s )

**obtained**by substituting go and po for d ; and Bi in [ t ] . The function K...

Page 1624

In the same way , the functions cos tvā

property cos svā cos tvāu ( da ) = 0 , s # t . ... Their first step consists in

an expression for f ( t , a ) as a “ linear combination " of the functions cos tva in

terms ...

In the same way , the functions cos tvā

**obtained**from the operator to enjoy theproperty cos svā cos tvāu ( da ) = 0 , s # t . ... Their first step consists in

**obtaining**an expression for f ( t , a ) as a “ linear combination " of the functions cos tva in

terms ...

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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