## Linear Operators: Spectral theory |

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Page 1010

PROOF . Let | | T | | A | | T | | B be the double norms of an operator when defined

in terms of the complete orthonormal systems { xæ , E A } , { YB , Be B }

Theorem IV .

PROOF . Let | | T | | A | | T | | B be the double norms of an operator when defined

in terms of the complete orthonormal systems { xæ , E A } , { YB , Be B }

**respectively**. By using the identity | x 2 = 26 | ( x , y ) ) 2 , which was proved inTheorem IV .

Page 1301

If d , d ' , and d " are the sums of the positive and negative deficiency indices of t , t

' , and ı '

the sum of the number of independent boundary values at a and the number of ...

If d , d ' , and d " are the sums of the positive and negative deficiency indices of t , t

' , and ı '

**respectively**, then d = d ' + d " — 2n . Proof . By Theorem 19 , d equalsthe sum of the number of independent boundary values at a and the number of ...

Page 1302

Nelson Dunford, Jacob T. Schwartz. Corollary 23 and from Theorems 19 and 20

that d ' and d ' exceed by n the number of independent boundary values at a and

at b

Nelson Dunford, Jacob T. Schwartz. Corollary 23 and from Theorems 19 and 20

that d ' and d ' exceed by n the number of independent boundary values at a and

at b

**respectively**. The statement of the present corollary is then evident .### What people are saying - Write a review

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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