## Linear Operators: Spectral operators |

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Page 2299

Hence we find that for n

Hence we find that for n

**sufficiently**large , each u in C is in p ( T + P ) and that R ( M ; T + P ) = B ( u ) . Since Blu ) is clearly the product of the compact operator R ( u ; T ) and a bounded operator , it follows that T + P is a ...Page 2300

E ( An ; T ) , then we have limp- . \ Ê , - Epl = 0. Since Ê , + 2x = E ( An ; T ) = 1,1 – Ê , has a finite dimensional range for all p . Thus , by Lemma VII.6.7 , I - E , has finite dimensional range for all

E ( An ; T ) , then we have limp- . \ Ê , - Epl = 0. Since Ê , + 2x = E ( An ; T ) = 1,1 – Ê , has a finite dimensional range for all p . Thus , by Lemma VII.6.7 , I - E , has finite dimensional range for all

**sufficiently**large p .Page 2394

Then there exists a solution oz ( t , u ) of the equation to = p ? o , defined for 0 St < oo and for all

Then there exists a solution oz ( t , u ) of the equation to = p ? o , defined for 0 St < oo and for all

**sufficiently**small u € P + , such that oz and os are continuous in t and u for 0 St < oo and u**sufficiently**small , and such that ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1931 |

Copyright | |

30 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 domain elements equation equivalent established exists extension 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