## Linear Operators: Spectral theory |

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Page 970

If Xe denotes the characteristic function of the set e in E , and if f is in L2 ( R ) , then Xef is in Ly ( R ) L2 ( R ) and f is the

If Xe denotes the characteristic function of the set e in E , and if f is in L2 ( R ) , then Xef is in Ly ( R ) L2 ( R ) and f is the

**limit**in the norm of L2 ( R ) of the generalized sequence { Xef } . Hence , by Theorem 9 , tf is the ...Page 1124

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

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

**limit**q ( E ) , then it follows from what we have already proved that En is an increasing sequence of projections and E , SE . If E is the strong**limit**of En , then E. SE and q ( E ...Page 1699

E - + by Lemma 3.22 , 9 £ fe is the

E - + by Lemma 3.22 , 9 £ fe is the

**limit**in the norm of H ( ) ( L ) of a sequence { g ; } of functions in CO ( L ) . Putting g ; ( x ) . 0 for x in Ce - L , it follows from Definition 3.15 that qeFe is the**limit**in the norm of H ( P ) ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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