## Linear Operators, Part 2 |

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Page 1027

... ET ) coincides with the trace of the restriction of the operator ET / ( T ) to the

finite dimensional space EH . PROOF . ( a ) Since H is infinite dimensional the

origin

the ...

... ET ) coincides with the trace of the restriction of the operator ET / ( T ) to the

finite dimensional space EH . PROOF . ( a ) Since H is infinite dimensional the

origin

**belongs**to the spectrum of both T and ET . Suppose that a # 0**belongs**tothe ...

Page 1116

Let the operator B be defined by Bqi ( Tqi ) yp / 2 ) -1 . Then plainly o Σ | Βφ.12 2 (

7 ? ! 2,2 < 0 , i = 1 so that , by Definition 6.1 , B

class Cz . If we let Aqi = y ! -p / 2 Pi , then A is plainly self adjoint and A

...

Let the operator B be defined by Bqi ( Tqi ) yp / 2 ) -1 . Then plainly o Σ | Βφ.12 2 (

7 ? ! 2,2 < 0 , i = 1 so that , by Definition 6.1 , B

**belongs**to the Hilbert - Schmidtclass Cz . If we let Aqi = y ! -p / 2 Pi , then A is plainly self adjoint and A

**belongs**to...

Page 1684

Then , if every partial derivative of F of order k

every partial derivative of F of order not more than m is continuous in the closure

of E. PROOF . By Corollary 2 and Hölder's inequality , each ( k - m ) th derivative ...

Then , if every partial derivative of F of order k

**belongs**to L ( EX ) , it follows thatevery partial derivative of F of order not more than m is continuous in the closure

of E. PROOF . By Corollary 2 and Hölder's inequality , each ( k - m ) th derivative ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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