## Linear Operators: Spectral theory |

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Page 955

Since h ( I ) = 1 for every ( complex - valued ) non - trivial multiplicative

that a multiplicative

to ...

Since h ( I ) = 1 for every ( complex - valued ) non - trivial multiplicative

**linear****functional**h , and since , by IX . 2 . 3 , every such function is continuous , it followsthat a multiplicative

**linear functional**on A is entirely determined by its restrictionto ...

Page 985

6 LEMMA . The closed

functions in a set S CL ( R ) coincides with the closed ideal determined by S .

Proof . First note that if f , geL ( R ) and pe L ( R ) then the

( y ) is a ...

6 LEMMA . The closed

**linear**manifold determined by the translates of thefunctions in a set S CL ( R ) coincides with the closed ideal determined by S .

Proof . First note that if f , geL ( R ) and pe L ( R ) then the

**function**p ( x ) / ( x - y ) g( y ) is a ...

Page 1303

B , ( g ) = $ 1 = w ; ( t ) f ( i ) ( t ) is a continuous

space D ( T1 ( ) ) . If lim _ ... Choose a function h in Co ( I ) which is identically

equal to one in a neighborhood of a and vanishes identically in a neighborhood

of b .

B , ( g ) = $ 1 = w ; ( t ) f ( i ) ( t ) is a continuous

**linear functional**on the Hilbertspace D ( T1 ( ) ) . If lim _ ... Choose a function h in Co ( I ) which is identically

equal to one in a neighborhood of a and vanishes identically in a neighborhood

of b .

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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