## Linear Operators: Spectral operators |

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Page 2299

Hence we find that for n

( ; T + P ) = Blu ) . Since B ( u ) is clearly the product of the compact operator R ( u

; T ) and a bounded operator , it follows that T + P is a discrete operator .

Hence we find that for n

**sufficiently**large , each u in Cn is in p ( T + P ) and that R( ; T + P ) = Blu ) . Since B ( u ) is clearly the product of the compact operator R ( u

; T ) and a bounded operator , it follows that T + P is a discrete operator .

Page 2300

Ê , - Epl = 0. Since , + = 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

Equ ; T + ...

Ê , - Epl = 0. Since , + = 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 . Since E is a countably additive spectral resolution , we haveEqu ; T + ...

Page 2394

Let the hypotheses of Corollary 2 be satisfied . Then there exists a solution oz ( t ,

x ) of the equation to = u o , defined for 0 St < oo and for all

+ , such that og and os are continuous in t and u for 0 St < oo and u

Let the hypotheses of Corollary 2 be satisfied . Then there exists a solution oz ( t ,

x ) of the equation to = u o , defined for 0 St < oo and for all

**sufficiently**small u e P+ , such that og and os are continuous in t and u for 0 St < oo and u

**sufficiently**...### 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 | 1929 |

Copyright | |

32 other sections not shown

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