## Linear Operators, Part 2 |

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Page 955

The letter E will

subsets of M , whose existence is asserted by Theorem X . 2 . 1 . Thus , for f in L (

R ) and g in L2 ( R ) , we have * g = Sx ( ) ( m ) E ( dm ) g . Since h ( I ) = 1 for

every ...

The letter E will

**denote**the projection - valued measure defined for the Borelsubsets of M , whose existence is asserted by Theorem X . 2 . 1 . Thus , for f in L (

R ) and g in L2 ( R ) , we have * g = Sx ( ) ( m ) E ( dm ) g . Since h ( I ) = 1 for

every ...

Page 1126

of the closed set C ; we shall

C ) . Since each projection in the spectral resolution of T and hence each

continuous function of T is a strong limit of linear combinations of the projections

Ei , it ...

of the closed set C ; we shall

**denote**this subspace of L , [ 0 , 1 ] by the symbol L (C ) . Since each projection in the spectral resolution of T and hence each

continuous function of T is a strong limit of linear combinations of the projections

Ei , it ...

Page 1673

( 12 ) the symbol qoM will

equation y ( x ) = 9 ( M ( x ) ) ; ( ii ) for each F in D ( 11 ) the symbol FoM - 1 will

for p in 07 .

( 12 ) the symbol qoM will

**denote**the function y in C ( 11 ) defined by theequation y ( x ) = 9 ( M ( x ) ) ; ( ii ) for each F in D ( 11 ) the symbol FoM - 1 will

**denote**the distribution G in D , ( 12 ) defined by the equation G ( q ) = F ( 9 0 M )for p in 07 .

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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