## 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 2068

It is clear that the linear space Lo = Lyn L.

It is clear that the linear space Lo = Lyn L.

**satisfies**( 11 ) . Also the space Lo = L , C of all integrable functions which coincide almost everywhere with ...Page 2112

An example is given to show that not every operator admits a duality theory of type 1 ; however , if T

An example is given to show that not every operator admits a duality theory of type 1 ; however , if T

**satisfies**the condition : ( a ) N ( F1 , T ) S M ( F2 ...Page 2399

It is readily verified that ôz ( t )

It is readily verified that ôz ( t )

**satisfies**tO2 = 0 , and also**satisfies**the second of the above asymptotic relationships .### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 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 function 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