## 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 2300

Then , since the collection of finite sums of projections E ( An ; T ) is

Then , since the collection of finite sums of projections E ( An ; T ) is

**uniformly**bounded , it is clear from [ * ] that the collection of finite sums of projections Elun ; T + P ) , n 2 K , is**uniformly**bounded .Page 2361

Thus , F * ( a ) is

Thus , F * ( a ) is

**uniformly**bounded for , in UN V , and hence , by the maximum modulus theorem , is**uniformly**bounded for , in U EN Uj . Since the set { U / } , i 2 N , covers the whole plane , with the possible exception of a bounded ...Page 2382

We shall now show that the second expression on the right of ( 14 ) converges to zero as lul → 00 , u remaining in P + ,

We shall now show that the second expression on the right of ( 14 ) converges to zero as lul → 00 , u remaining in P + ,

**uniformly**for 0 St < oo . Let { an } be a sequence of functions in Co [ 0 , 0 ) , each vanishing outside a bounded ...### 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