## Linear Operators: Spectral theory |

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Page 910

This

continuous . It therefore has a unique extension U from DL = H to the Ly - closure

of the set of bounded Borel functions , i.e. , to L ( u ) . An elementary continuity ...

This

**shows**that U preserves inner products and is thus one - to - one andcontinuous . It therefore has a unique extension U from DL = H to the Ly - closure

of the set of bounded Borel functions , i.e. , to L ( u ) . An elementary continuity ...

Page 985

It follows from Corollary II.3.13 that f * g is in for every g in L ( R ) , which

that L is an ideal and thus L 21 . Conversely let | be in the closed ideal f in L ( R )

and suppose that the bounded linear functional F vanishes on I. Then if the ...

It follows from Corollary II.3.13 that f * g is in for every g in L ( R ) , which

**shows**that L is an ideal and thus L 21 . Conversely let | be in the closed ideal f in L ( R )

and suppose that the bounded linear functional F vanishes on I. Then if the ...

Page 987

The preceding theorem

every h in L. Furthermore , since N is closed in the L ( R ) topology of L ( R ) , it

follows from Corollary V.3.12 that A is the conjugate - orthogonal complement of

L ...

The preceding theorem

**shows**that there is a point mo in Ř with h ( m . ) = 0 forevery h in L. Furthermore , since N is closed in the L ( R ) topology of L ( R ) , it

follows from Corollary V.3.12 that A is the conjugate - orthogonal complement of

L ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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