## Linear Operators: Spectral operators |

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Page 2403

We then use this inequality to

artificial setting , essentially to multiplication ... A first

made in this way , and immediately following upon this we develop a similar but ...

We then use this inequality to

**apply**Theorem 1 in an illustrative but somewhatartificial setting , essentially to multiplication ... A first

**application**( Theorem 6 ) ismade in this way , and immediately following upon this we develop a similar but ...

Page 2413

We may now

depending only on P , D , and c , such that the operators T and T + ( A ) are

similar whenever | | A | | < £ . Q . E . D . Theorem 1 and its corollaries are readily ...

We may now

**apply**Theorem 1 to conclude that there exists a positive constant εdepending only on P , D , and c , such that the operators T and T + ( A ) are

similar whenever | | A | | < £ . Q . E . D . Theorem 1 and its corollaries are readily ...

Page 2434

D . By using appropriate “ diagonalizing ” transformations ( cf . Theorem XII . 3 .

16 ) , we may

...

**Applying**Theorem 8 and Corollary 9 , the present theorem follows at once . Q . E .D . By using appropriate “ diagonalizing ” transformations ( cf . Theorem XII . 3 .

16 ) , we may

**apply**Theorem 21 to analyze a variety of operators . The following...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

29 other sections not shown

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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator discrete domain elements equation equivalent established exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero