## Linear Operators: Spectral theory |

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Page 1459

present corollary follows from Corollary 7 and Definition 25 ( b ) . Q . E . D . 31

Corollary . Suppose in addition to the hypotheses of Theorem 8 that the

coefficients Px ...

**PROOF**. It is obvious from Definition 20 that t is bounded below . Thus thepresent corollary follows from Corollary 7 and Definition 25 ( b ) . Q . E . D . 31

Corollary . Suppose in addition to the hypotheses of Theorem 8 that the

coefficients Px ...

Page 1724

Then T = S * and S = T *

suffices to show that ( T ) , g ) = ( f , Sg ) for f in D ( T ) and g in D ( S ) . By Green ' s

formula , proved in the last paragraph of Section 2 , this equation is valid if ...

Then T = S * and S = T *

**PROOF**. By the preceding lemma and by Corollary 11 itsuffices to show that ( T ) , g ) = ( f , Sg ) for f in D ( T ) and g in D ( S ) . By Green ' s

formula , proved in the last paragraph of Section 2 , this equation is valid if ...

Page 1750

We shall see , however , that this fact is needed in the course of the

Theorem 1 , and shall prove it by a direct method where it is needed . Remark 2 .

The theorem is false if no boundedness restriction is imposed on the coefficient ...

We shall see , however , that this fact is needed in the course of the

**proof**ofTheorem 1 , and shall prove it by a direct method where it is needed . Remark 2 .

The theorem is false if no boundedness restriction is imposed on the coefficient ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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