## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Page 2397

The theorem will follow as soon as it is shown that the

The theorem will follow as soon as it is shown that the

**hypotheses**of Theorem XVIII.2.34 are satisfied . In the notation of that theorem o ( T ) ...**Hypothesis**( i ) of Theorem XVIII.2.34 is satisfied by virtue of Corollaries 9 and 11.Page 2401

Using

Using

**hypothesis**( c ) , we may write this last equation as ( 5 ) P ( B - 4 ( B , A1 ) ) = ( A1 ) . Now , by**hypothesis**, the map B > * ( B , A1 ) of A → A has norm at most M2 ( M + M2 ) ...Page 2449

By

By

**hypotheses**( d ) and ( e ) , this last equation would follow from A +40 ( A , A ) — ¥ ( A , A1 ) = Aj ; thus , to solve ( 1 ) , we have only to ... Since , by**hypothesis**, 6M S1 , we have In + 1 = 2t , and our assertion follows .### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 other sections not shown

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### Common terms and phrases

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 countably additive defined Definition denote dense determined differential operator 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 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