## 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 1915

This was possible since it concerns a type of operator with a number of special properties including first order rate of growth of the

This was possible since it concerns a type of operator with a number of special properties including first order rate of growth of the

**resolvent**near the spectrum . Thus the reader whose primary interest is in the applications to such ...Page 1931

Here and else . where the symbol R ( $ ; T ) is used for the

Here and else . where the symbol R ( $ ; T ) is used for the

**resolvent**( $ I – T ) -1 of T at the point & in the**resolvent**set p ( T ) . If x is a vector in X , then by an analytic extension of R ( É ; T ' ) x will be meant an X ...Page 2590

( 2079 ) definition of , XV.3.9 ( 1936 ) existence of , XV.3.8 ( 1935 ) non - vanishing on open sets , XV.15.15 ( 2076 ) uniqueness of , XV.3.8 ( 1935 )

( 2079 ) definition of , XV.3.9 ( 1936 ) existence of , XV.3.8 ( 1935 ) non - vanishing on open sets , XV.15.15 ( 2076 ) uniqueness of , XV.3.8 ( 1935 )

**Resolvent**, of a spectral operator , XV.3 ( 1933 ) , XVI.1 ( A ) , ( B ) , ( C ) ...### 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