## Linear Operators: Spectral theory |

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Page 1064

... subsequence , we may

clear that gm ( x ) = g ( x ) for all x . Hence q = g , proving that ( gl , 51 , 111 , if f is

in Co ( I ) and vanishes outside a bounded set . Next let | be in L ( E ” ) , and let {

Im } ...

... subsequence , we may

**assume**that gm ( x ) = Q ( x ) for almost all x . But it isclear that gm ( x ) = g ( x ) for all x . Hence q = g , proving that ( gl , 51 , 111 , if f is

in Co ( I ) and vanishes outside a bounded set . Next let | be in L ( E ” ) , and let {

Im } ...

Page 1120

Throughout the present section , we

Hilbert space is separable . Subdiagonal representations of an operator are

connected with the study of its invariant subspaces . Thus , the key to the situation

that we ...

Throughout the present section , we

**assume**for simplicity of statement thatHilbert space is separable . Subdiagonal representations of an operator are

connected with the study of its invariant subspaces . Thus , the key to the situation

that we ...

Page 1734

Since we have only to show that ff is in H ( k + 1 ) ( UI ) for some neighborhood U

CU , of p , it is clear that we may

70 = 1 . This will be

Since we have only to show that ff is in H ( k + 1 ) ( UI ) for some neighborhood U

CU , of p , it is clear that we may

**assume**without loss of generality that U2 = U ,70 = 1 . This will be

**assumed**in what follows . Making use of the properties ( i ) ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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