## Linear Operators: Spectral theory |

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Page 970

Hence , by Theorem 9 , tf is the

sequence { t ( Xef ) } . Equivalently , we write tf [ x ... We now show that the

function f can be retrieved from tf by a similar

Hence , by Theorem 9 , tf is the

**limit**in the norm of L2 ( Mo ) of the generalizedsequence { t ( Xef ) } . Equivalently , we write tf [ x ... We now show that the

function f can be retrieved from tf by a similar

**limiting**procedure . 16 THEOREM .Page 1124

If En , E are in F and q ( En ) increases to the

we have already proved that En is an increasing sequence of projections and En

SE . If Em is the strong

If En , E are in F and q ( En ) increases to the

**limit**9 ( E ) , then it follows from whatwe have already proved that En is an increasing sequence of projections and En

SE . If Em is the strong

**limit**of En , then E. SE and q ( E . ) = Q ( E ) . Thus , it ...Page 1699

E by Lemma 3.22 , 9 € Ê . is the

} of functions in C ( L ) . Putting g ; ( x ) = 0 for x in Ce - L , it follows from Definition

3.15 that qeFc is the

E by Lemma 3.22 , 9 € Ê . is the

**limit**in the norm of H ( P ) ( L ) of a sequence { g ;} of functions in C ( L ) . Putting g ; ( x ) = 0 for x in Ce - L , it follows from Definition

3.15 that qeFc is the

**limit**in the norm of H ( P ) ( Ce ) of the sequence { g ; } of ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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