## Linear Operators, Part 2 |

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Page 932

Then there

additive ( resp . weakly countable additive ) function E on to B ( St ) such that if P

is the self adjoint projection of N onto H , then F ( e ) P = PE ( e ) P , for all e e . For

an ...

Then there

**exists**a Hilbert space N2 H and a self adjoint projection valuedadditive ( resp . weakly countable additive ) function E on to B ( St ) such that if P

is the self adjoint projection of N onto H , then F ( e ) P = PE ( e ) P , for all e e . For

an ...

Page 1189

The proofs of the remaining statements are left to the reader . Q.E.D. 6 LEMMA .

Let T be an operator in Hilbert space . Then ( a ) if D ( T ) is dense then T * is a

closed linear operator ; ( b ) if T - 1

...

The proofs of the remaining statements are left to the reader . Q.E.D. 6 LEMMA .

Let T be an operator in Hilbert space . Then ( a ) if D ( T ) is dense then T * is a

closed linear operator ; ( b ) if T - 1

**exists**with dense domain then ( T * ) - 1**exists**...

Page 1400

Then the deficiency indices of t are both equal to an integer k and ( a ) for every

self adjoint extension T of To ( t ) , the dimension of the null - space { Tf = af is at

most k ; ( b ) there

...

Then the deficiency indices of t are both equal to an integer k and ( a ) for every

self adjoint extension T of To ( t ) , the dimension of the null - space { Tf = af is at

most k ; ( b ) there

**exist**self adjoint extensions T of T. ( t ) such that 1 & 0 ( T ) ; ( c )...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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